The NuTeV collaboration reported anomalously large weak mixing angle sin 2 θW in comparison with the standard model prediction. Neutrino and antineutrino charged-and neutral-current events are analyzed for extracting sin 2 θW . Although the Paschos-Wolfenstein relation is not directly used in the analysis, it plays an important role in the determination. Noting that the target nucleus, iron, is not an isoscalar nucleus, we derive a leading-order expression for a modified Paschos-Wolfenstein relation for nuclei, which may have neutron excess. Then, using charge and baryon-number conservations for nuclei, we discuss a nuclear correction in the sin 2 θW determination. It is noteworthy that nuclear modifications are different between valence up-and down-quark distributions. We show this difference effect on the NuTeV sin 2 θW deviation.