In this paper we propose an iterative algorithm, which is based on the Krasnoselskii-Mann iterative algorithm for fixed point problems of a finite family of demicontractive map-pings in the setting of real Banach spaces. We prove that the sequence generated by the proposed method converges strongly to a common fixed point of a finite family of demicontractive mappings which is also the solution of a variational inequality. The iterative algorithm and results presented in this paper generalize, unify and improve some previously known results of this area.