Recently, the cathode-like luminescence phenomena are observed from the surface of solid dielectrics under steady-state high voltage excitation in vacuum, which is closely related to the self-stabilizing secondary electron emission (SSEE) occurring on insulator surface. In this paper, the theoretical analysis about surface charging based on the SSEE is made, and a one-dimensional Mont Carlo simulation on surface charge accumulation under DC voltage excitation is provided. The results reveal that surface charging process can be divided into three stages including initial accumulation, fast multiplication, and final stable stage. In the final stage, the SSEE phenomena are achieved and surface charges are invariable and reach up to a stable distribution. The simulated stable surface charge distribution is consistent with the theoretical deduction results, which confirms the existence of SSEE process.