As a porous material, the strength and deformation characteristics of cement after well-completion are related to internal pores. This article describes a damage law of cement with pores. The damage law was applied to a damage response analysis of a gas storage salt cavern wellbore during the service period. The damage is caused by two aspects: the initial isotropic damage caused by the primary pores, and the subsequent anisotropic damage caused by the secondary micro-cracks in the matrix. It is necessary to establish a damage evolution model including the effects of pores and micro-cracks. Triaxial compression tests are performed on two sets of cement samples with and without pores to verify the model. By user programmable features (UPFs) in the finite element software ANSYS, the damage constitutive equation is embedded in a numerical calculation. According to the structure and load parameters of a salt cavern in Jintan, a wellbore model with porous cement sheath was established for engineering application. The following conclusions are obtained through experiments and numerical calculations: the pores reduce the strength of cement under low confining pressure but increase the deformability under high confining pressure. If there are no pores in the cement sheath, high damage areas are easily formed at the internal interface. When the porosity becomes 5%, the radial deformation ability is enhanced, and the interface is not easy to debond. However, when the porosity increases to 7.5%, the radial micro-cracks between the pores are formed, resulting in radial destruction.