According to court filings, TigerDirect is seeking an injunction to stop Apples from using the word "tiger" online or in printed materials.
The lawsuit, filed in the United States District Court for the District of Florida, also claims that Apple engaged in deceptive and unfair trade practices. TigerDirect says Apples use of Tiger "is causing confusion, mistake and deception among the general purchasing public."
The retailer owns trademarks on Tiger, TigerDirect and TigerSoftware, which appear in 25 million catalogs each year.
TigerDirects main contention is that Apple has flooded the Internet with the word "tiger" as it relates to computers, which has knocked the retailer from the top of search results on Google, Yahoo and MSN.
"Apple Computer has created and launched a nationwide media blitz led by Steven Jobs, overwhelming the computer world with a sea of Tiger references," the lawsuit says.