A gravity-incorporated standard model is constructed in a generalized differential geometry (GDG) on R₄×X₂. Here, R₄ and X₂ are the four-dimensional Riemann space and two-point discrete space, respectively. A GDG on R₄×X₂ is constructed by adding the basis χ_n (n = 1,2) of the differential form on X₂ to the ordinary basis dx^µ on R₄, and so it is a direct generalization of the differential geometry on the continuous manifold. A GDG is a version of non-commutative geometry (NCG). We incorporate gravity by simply replacing the derivative _µ by the covariant derivative _µ + ω_µ for a general coordinate transformation in the definition of the generalized gauge field on R₄×X₂, keeping other parts unchanged. The Yang-Mills-Higgs Lagrangian for the standard model is obtained by taking the inner product of two generalized field strengths, whereas the Einstein-Hilbert gravitational Lagrangian is created by the inner product of a generalized field strength and a tensor {E^a}_b on local Lorentz space.