In order to reduce the computational cost, the basis functions are defined only on the boundary curve for bodies of revolution (BORs). A marching-on-in-degree (MOD) based time-domain electric field integral equation (TD-EFIE) method is proposed to analyze the transient electromagnetic scattering from perfectly electric conducting BORs with open structures. Moreover, the MOD method for the time domain combined field integral equation (TD-CFIE) is used to obtain the induced currents on closed BORs in this paper. Numerical results are presented to demonstrate the efficiency and the stability of the proposed method for the electromagnetic scattering from perfectly electric conductor BORs.