Apple Corps, owned by Paul McCartney, Ringo Starr, John Lennon's widow, Yoko Ono, and the estate of George Harrison, argued that the computer company had violated a 1991 trademark agreement by moving into the music business through its iTunes online store.
Apple Computer argued in court hearings in London this year that iTunes was primarily a data transmission service, which is permitted by the agreement.
The 1991 out-of-court settlement, which included a $26 million payment by Apple Computer, set out areas in which each party would have exclusive use of their respective fruit-shaped logos.
Justice Mann said: "I find no breach of the trademark agreement has been demonstrated. The action therefore fails."
Apple Corps said it would appeal the decision, while Apple Computer was awarded court costs.