<p>This study investigates a postprocessing method for enhancing the accuracy of numerical solutions to the Cahn–Hilliard equation. The present research mainly focuses on the fully discrete case, although the semi discrete case of the Cahn–Hilliard equation has been analyzed previously. The temporal discretization uses the backward Euler method, while spatial discretization is based on finite elements. The approximations are postprocessed by solving two decoupled Poisson equations with data based on the Galerkin approximation in an enriched finite element space (either on a finer grid or a higher-order space), when the fully discrete standard Galerkin approximation is computed at any fixed time on a coarser space. We prove that the temporal errors of the fully discrete Galerkin approximation and the postprocessed approximation are asymptotically equivalent. Additionally, the enhanced spatial precision of the postprocessing technique is unaffected by errors introduced by the time-stepping scheme. The new developments in this paper also include their applications to a posteriori error estimate of variable step-size backward Euler method for Cahn–Hilliard equation.</p>