Abstract： This paper is concerned with the existence problem of periodic solutions for a normal and tumor cells competition model with impulsive effects.The mathematical problem involves a coupled system of Lotka-Volterra together with periodically pulsed conditions.The approach to the problem is by the method of upper and lower solutions and its associated monotone iterations.This method is constructive and the periodic solutions can becomputed from a linear iteration process in the same fashion as for impulsive differential equation initial value problem.a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions.