SHENZHEN, China » Zhong Guoyan sifted through piles of fish at a Wal-Mart in Shenzhen, one of China’s largest cities. She studied the fins, to make sure they were bright red and firm. She peered at the eyeballs — were they bulging?

“When I come here, I have a look,” she said. “If it’s good, then I will buy it. If it’s only cheap, I won’t buy it.”

In American Wal-Marts, customers don’t get to fondle their fish. But America is not China, as the world’s biggest retailer has learned. If the Arkansas-based company wants to win over foreign consumers, it has to shed some of its American ways, and cater to very different customs and conventions that are fast changing.

Zhong eventually tossed a couple of fish into a plastic bag — a small victory in Wal-Mart’s struggle to build an international empire.

The stakes are high: The company can’t count on much growth in the U.S. — it’s facing challenges at home with intense competition from Amazon.com and dollar stores — so the retailer is depending more on its operations overseas.

China is the ultimate prize. The Chinese grocery market, already the world’s largest at $1.1 trillion a year, is expected to grow to $1.5 trillion in sales in just the next four years, says IGD, a global consumer products research firm.

“China remains a strategic market for our future,” Doug McMillon, CEO of Wal-Mart Stores Inc. recently told investors.

Getting the food business right is critical for Wal-Mart. Shoppers buy groceries more often than anything else. If Wal-Mart can get them in the door to buy food regularly, perhaps they will visit more frequently for items like pajamas and coffee makers — and eventually become loyal online customers, too.

The company has taken some lumps trying to cross borders in food retailing. Overall international sales growth dropped 9.4 percent last year largely because of the strong dollar. And while Wal-Mart’s overseas business had a strong start to this year, it faces long-term challenges. Wal-Mart gave up in Germany and South Korea in 2006. It’s closing stores in Brazil.

Overseas, Wal-Mart lacks the scale to squeeze local suppliers on price as it does in the U.S. It also faces nimble competitors. And it has struggled to duplicate its bedrock strategy of constant bargains.

But Wal-Mart has learned over the years from its missteps, discovering that it needs to adapt to local ways and that patience pays off.

In Mexico, Canada and Japan, it’s won shoppers over time. In Chile, it launched a corporate culture campaign and worked closely with suppliers to coax them into its way of doing business.

“Wal-Mart,” says Bryan Roberts of the London retail consultancy TCC Global, “is a very determined organization.”

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WINNING OVER PICKY CONSUMERS

In the unruly Chinese market, some competitors cut corners, mislabeling products or even selling tainted foods. The risks have made Chinese consumers unusually wary.

Sean Clarke, CEO of Wal-Mart China, based in Shenzhen, previously worked in Britain, Japan, Germany, and Canada. China, he says, “is easily the most challenging market to operate … There is a huge level of distrust.”

Wal-Mart had a difficult time promoting “everyday low prices” — promising the lowest prices on a basket of goods every time consumers shop.

Some rivals poached the “everyday low price” message, confusing customers. Wal-Mart scrambled to find the right slogan. In 2012, it introduced “Worry Free” — implying quality and reassuring shoppers who worry that deals will expire before they get to the store.

The company’s message: Efficiency and good management, not cutting corners, make everyday low prices possible.

The message has sometimes been muddled. When Wal-Mart came to China, it was slow to tailor its offerings to local tastes. Realizing its mistake, Wal-Mart gave local managers more leeway to run their businesses.

But that approach backfired, leading to a series of food-safety violations. In one particularly embarrassing episode, Wal-Mart had to recall donkey meat — a delicacy in China — after DNA testing showed it contained traces of fox meat.

In response, Wal-Mart slashed nearly two-thirds of its 20,000 suppliers. Now, Wal-Mart knows exactly where each product comes from. Wal-Mart also took back some of the responsibilities from local managers and increased its investment in food safety. It introduced mobile testing labs that check for pesticides on vegetables and fruit and employed handheld devices to check temperatures of meat products.

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GAINING CONTROL OVER SUPPLIERS, COSTS

In America, Wal-Mart has the clout — 25 percent of the U.S. grocery business— to force suppliers to do things the Wal-Mart way. That means cutting costs to the bone. In return, the suppliers enjoy steady demand from Wal-Mart, so they don’t have to spend so much on advertising or worry about paying extra costs to staff their factories to meet unexpected peaks in demand.

In China, things are tougher. Wal-Mart accounts for just 2.3 percent of the grocery market. Ninety-five percent of all products Wal-Mart sells in China are supplied by local companies.

The Chinese supply chain is also notoriously inefficient. For years, Wal-Mart and other foreign companies didn’t deal directly with their suppliers, working mostly instead through a labyrinth of middlemen.

Three years ago, Wal-Mart decided to cut out the middlemen and route as many goods as possible through 20 of its own distribution centers.

By eliminating the go-betweens, Wal-Mart could negotiate directly with suppliers and knock down costs — often by 10 percent or more.

The change also gives Wal-Mart more control over the quality of the food being sent to its stores and the efficiency with which it gets to them. Before the switch, only about 75 percent of orders would actually reach Wal-Mart stores; now 95 percent do.

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FIGHTING COMPETITORS

Wal-Mart landed in China in 1996, a year behind Carrefour, opening two stores in Shenzhen— a Wal-Mart supercenter and a Sam’s Club. They were the first foreign retailers to offer the big-box shopping experience, which offers everything from clothing to food. After investing in a Taiwanese-owned retail chain in 2007, Wal-Mart became China’s biggest super-sized store chain and expanded its lead for the next two years.

But local and regional competitors quickly closed the gap, sometimes undercutting Wal-Mart prices because they have closer ties to local suppliers and can negotiate better deals.

Wal-Mart insists its market share for the big-store sector has increased over the past three years. But Euromonitor says Wal-Mart’s market share has fallen to 9.6 percent (No. 3 in the market) after peaking at 11.6 percent in 2009.

Wal-Mart last year announced plans to add 115 stores in China by 2017, bringing the store count to 530. It’s concentrating in markets where it’s already established, including its stronghold in the south. And it has given up on about 30 lackluster stores.

Meanwhile, Wal-Mart faces another challenge in China, and it is not from other big box stores.

Across the globe, shoppers are increasingly buying online or at small stores. But in China, that trend is more dramatic. It has already overtaken the U.S. as the world’s biggest online marketplace.