Let C be nonempty closed convex subset of real Hilbert space H . Consider C a nonexpansive semigroup ℑ = { T ( s ) : s ≥ 0 } with a common fixed point, a contraction f with coefficient 0 < α < 1 , and a strongly positive linear bounded operator A with coefficient γ ¯ > 0 . Let 0 < γ < γ ¯ / α . It is proved that the sequence { x n } generated iteratively by x n = ( I − α n A ) ( 1 / t n ) ∫ 0 t n T ( s ) y n d s + α n γ f ( x n ) , y n = ( I − β n A ) x n + β n γ f ( x n ) converges strongly to a common fixed point x ∗ ∈ F ( ℑ ) which solves the variational inequality 〈 ( γ f − A ) x ∗ , z − x ∗ 〉 ≤ 0 for all z ∈ F ( ℑ ) .