Let C be a nonempty closed convex subset of real Hilbert space H and F = ${S(t):t{geq}0}$ a nonexpansive self-mapping semigroup of C, and $f:C{ ightarrow}C$ is a fixed contractive mapping. Consider the process {$x_n$} : $${{x_{n+1}={eta}_nx_n+(1-{eta}_n)z_n\z_n={alpha}_nf(x_n)+(1-{alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$$. It is shown that {$x_n$} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.