The co-founder and creative director of advertising firm Strawberry Frog, Scott Goodson, said his company is named after an extremely rare species of reptile that is red with blue legs and lives in the Amazon rainforest.

“Frogs are smarter and faster than the big, slow dinosaurs we compete against,” said Mr. Goodson. “The frog versus the dinosaur is 21st-century thinking versus 20th-century thinking.”

Strawberry Frog is one of the few advertising agencies actually located these days on Madison Avenue, but its unorthodox strategy sets it apart. For starters, the firm is pet friendly and employees can bring their dogs or cats with them every day. The dress code is hip, the red-and-lime décor is funky and its staff of 125 people come from 14 countries.

But what’s most unusual is that this relatively small firm has been able to woo some of the world’s biggest clients out of the arms of its gigantic, multinational advertising competitors. Last month, it beat out the biggest by landing as a client Sam’s Club, a division of Wal-Mart.

“We selected Strawberry Frog because they offered the greatest strategic insight, game-changing creativity, and vision for the future of Sam’s Club,” the marketing executive and vice president of Sam’s Club, Mark Goodman, said in an interview with AdWeek.

But the firm has been turning heads ever since 2000 when it landed the Mitsubishi Motors account in 42 countries with billings today estimated at $250 million. “We pitched for Mitsubishi’s business against the biggest in the world and we won to everyone’s surprise,” said Mr. Goodson.

Besides the car company, Strawberry Frog is also the agency of record for Unisys in 25 countries, Credit Suisse, beverage giant Diageo, and Heineken in 155 countries. It is able to service these huge companies by deploying what Mr. Goodson calls the hub-and-spoke business model. Like Hollywood’s film business, Strawberry Frog doesn’t employ an army of actors, writers, artists, directors, and other consultants. It hires teams to work on specific projects on a freelance basis and devises campaigns that cross all borders.

The firm’s Mitsubishi campaign, for its four-wheel-drive Outlander model, resulted in a jump in worldwide sales after Strawberry Frog worked to create a new “brand culture.”