We consider the cohomological classification of the (4 + 2)-dimensional topological field which was proposed by Luscher, for the SU(2)(L) x U(1)(Y) electroweak theory. The dependence on the admissible abelian gauge field of U(1)(Y) is determined through topological argument, with the SU(2)(L) gauge field fixed as background. We then show the exact cancellation of the local gauge anomaly of the mixed type SU(2)(L)(2) x U(1)(Y) at a finite lattice spacing, as well as U(1)(Y)(3), using the pseudo reality of SU(2)(L) and the anomaly cancellation conditions in the electroweak theory given in terms of the hyper-charges of U(1)(Y), (C) 2001 Elsevier Science B.V. All rights reserved.