Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm.We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space.The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory.The self-consistent equation for the pair potential is derived and solved.Somewhat contrary to expectation,a weak attractive U comparable to the pair potential can destroy the superconductivity,whereas for weak to intermediate repulsive U,the pair potential can be enhanced.The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation.We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors,in contrast to the uncorrelated BCS limit.