Abstract: Based on the relaxed projection method,the author uses a hyperplane to substitute for the convex set and makes full use of the calculated  bestparameter.A new algorithm named m-steps modified relaxed projection method  is constructed to solve the convex feasibility problem.Furthermore,the algorithm is proved to be strong convergence.

Key words: convex feasibility problem, relaxed projection method, m-steps modified relaxed projection method, weakly convergence, strong convergence