Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $ ightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $ ightarrow$ K be a contraction mapping. Let {$alpha_n$} and {$eta_n$} be sequences in (0, 1) such that $lim_{x{ ightarrow}0}{alpha}_n=0$, (0.1) $sum_{n=0}^{infty};{alpha}_n=+{infty}$, (0.2) 0 < a ${leq};{eta}_n;{leq}$ b < 1 for all $n;{geq};0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0;{in};K$, $y_n;=;{alpha}_{n}f(x_n)+(1-alpha_n)x_n$, $n;{geq};0$, $x_{n+1}=(1-{eta}_n)y_n+{eta}_nTy_n$, $n;{geq};0$, (0.4) converges strongly to a point p $in$ Fix(T} which satisfies the variational inequality <p - f(p), p - z> $leq$ 0, z $in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.