Periodic solutions of reaction-diffusion systems with time delays are investigated. It is constructed that the - per and lower control function of nonmonotone reaction term, and it is showed that the function satisfies a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. By using the method of upper and lower solutions and fixed point theorem, it is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled-upper and lower solutions. Some methods for proving the stability of the periodic solution are also given. And some known resuits are extended.