  Based upon the mathematical formulas of Lattice gauge theory and
non-commutative geometry differential calculus, we developed an approach of
generalized gauge theory on a product of the spacetime lattice and the two
discrete points(or a $Z_2$ discrete group). We introduce a differentiation for
non-nearest-neighbour points and find that this differentiation may lead to the
introduction of Wilson term in the free fermion Lagrangian on lattice. The
Wilson-Yukawa chiral model on lattice is constructed by the generalized gauge
theory and a toy model and Smit-Swift model are studied.
