The diode insulator applied in the Tesla-type pulsed power generator has been simulated. It is found that the field-enhancement regions are generally the breakdown regions. The reasons responsible for breakdown are explored from the aspects of electric-field distribution, angle distribution of electrical lines relative to insulator surfaces, and the imperfections in the insulator, etc. It is believed that the imperfections are the main factor responsible for breakdown, and the local field enhancement and improper structure design are factors partly leading to breakdown. The key structures on the coaxial line influencing the electric field distribution of insulator interfaces are optimized. Then the optimum ranges for the radii of the anode chamfer and the cathode shield are summarized.