A　Predator-Prey　system　is　proposed　with　an　introduction　of　anorexia　response　on　one　prey　population.　By　using　the　comparison　theorem　and　constructing　suitable　Lyapunov　function,　we　study　such　Predator-Prey　system　with　almost　periodic　coefficients.　Some　sufficient　conditions　are　obtained　for　the　existence　of　a　unique　almost　periodic　solution.　Numerical　simulations　of　Predator-Prey　system　with　anorexia　response　and　the　one　without　anorexia　response　are　performed.　Our　observations　suggest　that　anorexia　response　on　one　prey　population　has　a　destabilizing　effect　on　the　persistence　of　such　Predator-Prey　system.　©　2005　Elsevier　Ltd.　All　rights　reserved.