Optically pumped terahertz (THz) lasers with high pulse repetition frequency are designed. Such a laser includes two parts: the optically pumping laser and the THz laser. The structures of the laser are described and analyzed. The rate equations for the pulsed THz laser are given. The kinetic process and laser pulse waveform for this kind of laser are numerically calculated based on the theory of rate equations. The theoretical results give a helpful guide to the research of such lasers.