Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${{T_i}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F;=;{cap}^N_{i=1}F(T_i);{ eq};{ heta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${{T_i}}^N_{i=1}$ is semi-compact. Let ${{alpha}_n};{subset};[{delta},;1-{delta}]$ for some ${delta};{in};(0,;1)$ and ${{eta}_n};{subset};[ au,;1]$ for some ${ au};{in};(0,;1]$. For arbitrary $x_0;{in};K$, let the sequence {$x_n$} be defined iteratively by ${{x_n;=;{alpha}_nx_{n-1};+;(1-{alpha}_n)T_ny_n,;;;;;;;;; atop {y_n;=;{eta}nx_{n-1};+;(1-{eta}_n)T_nx_n},;{forall}_n{geq}1,}$, where $T_n;=;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${{T_i}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${eta}_n;{equiv};1$ or N=1 are also new.