The company said Apple's use of Tiger had a negative impact on its ability to market its products to its customers since Apple Tiger talk tweaked search engine results.
TigerDirect says it owns trademarks on the names Tiger, TigerDirect and TigerSoftware.
It charges that Apple's branding of its new OS is "causing confusion, mistake and deception among the general purchasing public".
News service Bloomberg said Tiger Direct, a Systemax subsidiary, is seeking an injunction against the Apple Tiger, though time is running out. ยต