Summary: A fully discrete difference scheme to the 3D nonlinear Sobolev-Galpern equation with Dirichlet initial-value boundary conditions is presented. The unique solvability of the numerical solution is shown by using discrete space functional analysis and the energy estimate method. The long-time stability and convergence of the scheme are proved. Furthermore, the existence of a global attractor for the discrete dynamical system and the upper semicontinuity \(d(\mathcal{A}_{h,\tau},\mathcal{A})\to 0\) are proved. Results show that the difference scheme can effectively simulate infinite dimensional dynamical systems.