A simple post-processing technique for fifinite element methods with L2-superconvergence is proposed. It provides more accurate approximations for solutions of twoand three-dimensional systems of partial differential equations. Approximate solutions can be constructed locally by using fifinite element approximations uhprovided that uhis superconvergent for a locally defifined projection Phu. The construction is based on the least-squares fifitting algorithm and local L2-projections. Error estimates are derived and numerical examples illustrate the effectiveness of this approach for fifinite element methods.