Abstract： The mathematical model of two competing species dynamical system in a periodically changing environment with diffusion and instantaneous changes in the population densities is investigated. The model is described by a coupled system of reaction-diffusion equations together with some initial boundary value and impulses conditions. The upper-lower Solution method is established and some comparison principles are obtained. The asymptotic prope. rties of the system are researched by using the comparison theorem of impulsive ordinary differential equations and using the solutions of dominating inpulsive ordinary differential equation to control and estimate the solutions of the system.