In this paper, we introduce a new two-step iteration process to approximate common fixed points of two nonexpansive mappings in Banach spaces and established strong and weak convergence results of this iterative scheme. We also shows that our iteration process converges faster than of Mann, S-iterative and modified Ishikawa processes. Our result also illustrated with help of an example with numerical calculation. The results obtained in this paper is generalizations of Sahu [7].