Let $C$ be a closed convex subset of a Banach space. In this paper, we construct a three-step iteration process $\{x_n\}$ with errors for three nonlinear mappings $S,T,U\colon C\to C$ given by: $x_1\in C, \ z_n=\alpha_n''x_n+\beta_n''U^nx_n+\gamma_n''w_n,\ y_n=\alpha_n'x_n+\beta_n'T^nz_n+\gamma_n'v_n,\ x_{n+1}=\alpha_nx_n+\beta_nS^ny_n+\gamma_nu_n$, for all $n\geq 1$ and prove a strong convergence theorem under a modified Senter and Dotson's condition (A). This improves Xu and Noor's result in 2002. Further, we generalize a Khan and Fukhar-ud-dim's result in 2005.