Zimmerman says in an appeal filed Tuesday that he fears Circuit Judge Kenneth Lester Jr. is biased against him and he wants a new judge to handle his case.
Zimmerman is charged with second-degree murder in the Feb. 26 death of Martin, 17, of Miami Gardens in a gated community in Sanford.
Zimmerman has pleaded not guilty, saying he acted in self-defense.
The appeal was filed with the 5th District Court of Appeal in Daytona Beach.
All proceedings in Zimmerman's case will be delayed until that court decides whether to hear the appeal.
The lack of an arrest for 45 days led to protests around the nation.