The left–right symmetric gauge model with the symmetry of SU(3)_c × SU(2)_L × SU(2)_R × U(1) is reconstructed in the generalized differential geometry (GDG) on the product space of Minkowski space M₄ and four-point discrete space X_N with N 4. Ordinary gauge fields are regarded as the connection on M₄; on the other hand, Higgs boson fields are regarded on the discrete space X_N. This is a common view in the non-commutative geometry initiated by Connes. Gauge and Higgs fields are described in this paper as connections with the 1-form base on M₄ × X_N, a situation which is more similar to the ordinary differential geometry. We explain this formulation based on the matrix representation by use of the N × N matrix form. In addition to the generalized field strength obtained from the generalized gauge field, the anomalous field strength is introduced to yield sufficient Higgs potential and interacting terms by combining with corresponding terms in the generalized field strength. The resultant Higgs potential terms deduce the particular mass pattern such that among the Higgs doublet bosons, one CP-even scalar boson survives in the weak energy scale and the other four scalar bosons acquire the mass of the SU(2)_R × U(1) breaking scale.