Let K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping, and let { T i } i = 1 ∞ be an infinite countable family of asymptotically nonexpansive mappings with the sequence { k i n } satisfying k i n ≥ 1 for each i = 1 , 2 , … , n = 1 , 2 , … , and lim n → ∞ k i n = 1 for each i = 1 , 2 , … . In this paper, we introduce a new implicit iterative scheme generated by { T i } i = 1 ∞ and prove that the scheme converges strongly to a common fixed point of { T i } i = 1 ∞ , which solves some certain variational inequality.