The equation of state of the asymmetric nuclear matter is calculated with the Gogny D1 effective density-dependent nucleon-nucleon interaction and the Coulomb interaction in the framework of the finite-temperature HF method with the rearrangement term. The dependence of the thermodynamical properties such as the critical temperature of the liquid-gas phase transition, the chemical potential, the compression modulus and the entropy on the Coulomb interaction in nuclear matter is treated by using a shielded two-body Coulomb potential and this method has been found to be a reasonable and effective approach.