The second-biggest global sportswear group after Nike, Adidas filed a motion with a court in the US state of Oregon, home to its US headquarters, charging that Wal-Mart copied models of Adidas footwear, the German business daily Handelsblatt reported.
Wal-Mart used a striped logo similar to the one associated with Adidas products, displaying two or four stripes whereas the German company's trademark is three, the Adidas spokeswoman said.
She did not provide further details.
Adidas recently won a lawsuit against a US maker of sports shoes for the same reason and obtained $305 million from an Oregon court in damages and interest, Handelsblatt said.
It added that hearings in the new suit would begin on October 6.