Abstract: The Crank-Nicolson(CN) fully discrete scheme of conforming Galerkin finite element method was mainly studied for the nonlinear parabolic integro-differential equation. By estimating the nonlinear term rigorously and using combination trick of the interpolation and projection, the supercloseness of order O(h²+τ²) in L^∞(H¹) norm was derived. Further, the global superconvergence result was obtained through interpolated post-processing technique, which covers the shortage in the previous literature. At the same time, a numerical example was provided to verify the correctness of the theoretical analysis and the high efficient of the proposed method.