Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0;{in};C$ arbitrarily chosen, $x_{n+1};=;{alpha}_n{gamma}f(W_nx_n)+{eta}_nx_n+((1-{eta}_n)I-{alpha}_nA)W_nP_C(I-s_nB)x_n$, ${forall}_n;{geq};0$, where $gamma$ > 0, B : C $ ightarrow$ H is a $eta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $alpha$ (0 < $alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${ldots}$, $T_N$ and {$lambda_{n,1}$}, {$lambda_{n,2}$}, ${ldots}$, {$lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q;{in};F$ := $igcap^N_{i=1}F(T_i);igcap;VI(C,;B)$ which solves the variational inequality $langle({gamma}f;-;A)q,;p;-;q{ angle};{leq};0$ for all $p;{in};F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.