Let $E$ be a uniformly convex Banach space, $C$ be a nonempty closed convex subset of $E$, and $T:C\rightarrow C$ be an asymptotically nonexpansive mapping with fixed points. It is shown that under some suitable conditions, the sequence $\{x_n\}$ defined by the modified Ishikawa iteration process: $x_{n+1}=rp_n, p_n=(1-a_n)x_n+a_nT^{m_n}ry_n+u_n$, $y_n=(1-b_n)x_n+b_nT^{k_n}x_n+v_n$, $(n\geq 1)$ converges weakly to a fixed point of $T$.
