To obtain a more comprehensive knowledge of the surface electric field distribution of composite insulators, a three-dimensional (3D) simulation model of a 10 kV FXBW4-10/70 composite insulator was established, and the distribution of the axial and radial electric fields on the surface of the insulator under normal, damaged, internal defect, and fouling fault conditions were calculated and analyzed based on the finite element method. The results showed that the axial and radial electric field distributions on the surfaces of the normal composite insulators were “U” shaped, the radial electric field at the damaged location had a greater change than the axial electric field, and both the axial and radial electric fields at the internal defect location increased significantly. For the insulator covered with NaCl conductive fouling, the axial electric fields at the high-voltage (HV) and low-voltage (LV) ends showed a greater change. The results can provide a basis for the fault identification of composite insulators and the optimal design of insulation structures.