Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X . Let T : C → C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L -Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point of T .