  We investigate a possible nuclear correction to the NuTeV measurement of the
weak-mixing angle sin^2 theta_W. In particular, a nuclear modification
difference between u_v and d_v distributions contributes to the NuTeV
measurement with the iron target. First, the modification differenceis
determined by a chi^2 analysis so as to reproduce nuclear data on the structure
function F_2 and Drell-Yan processes. Then, taking the NuTeV kinematics into
account, we calculate a contribution to the sin^2 theta_W determination. In
addition, its uncertainty is estimated by the Hessian method. Although the
uncertainty becomes comparable to the NuTeV deviation, the effect is not large
enough to explain the whole NuTeV sin^2 theta_W anomaly at this stage. However,
it is difficult to determine such a nuclear modification difference, so that we
need further investigations on the difference and its effect on the NuTeV
anomaly.
