Abstract: For the application requirements of the high voltage pulse generator based on the pulse forming network(PFN) in the microwave driver and the solid-state modulator, the theory of the PFN with the trapezoidal pulse output was developed. First, the analytical expression of the trapezoidal pulse was obtained by the Prony algorithm. Secondly, the waveform parameters were optimized by using the best uniform approximation algorithm based on the equations of the optimal control with the maximum and minimum of the output wave, and solving these nonlinear equations with the Newton iteration method or other numerical methods. Then, the initial parameters of the PFN were worked out with the method of impedance matching. The final components parameters were obtained by rejecting some secondary parameters and adjusting a few of the main parameters. The method and criteria of the design for a PFN with the low ripple trapezoidal pulse output were proposed by theoretical analysis and numerical simulation. The results show that the proposed method can be used to design the PFN with any order and low ripple, and it can be used to design not only the pulse source with trapezoidal pulse output, but also the pulse sources with other pulse output.