It is proved that the three-step iteration sequence converges strongly to a fixed point for nonself asymptotically quasi-nonexpansive type mappings in Banach space. The results obtained in this paper extend and improve the recent ones announced by S.S. Chang and Y.Y. Zhou[2] , S. Quan, S.Chang and J.Long [13] , W. Nilsrakoo, S. Saejung [10] and many others.