In this paper, we investigate the problem of finding a common element of the solution set of a general system of variational inequalities, the solution set of a convex feasibility problem and the fixed point set of a strict pseudocontraction in a real Hilbert space. Based on the well-known extragradient method, viscosity approximation method and Mann iterative method, we propose and analyze a new relaxed extragradient method for computing a common element. Under very mild assumptions, we obtain a strong convergence theorem for three sequences generated by the proposed method. Our proposed method is quite general and flexible and includes the iterative methods considered in the earlier and recent literature as special cases. Our results represent the modification, supplement, extension and improvement of some corresponding results in the references.