Abstract: The requirement for truncating the open boundary of waveguide used in the simulation of high power microwave (HPM) sources was discussed. The characteristics of different types of perfectly matched layer (PML) was analyzed, and the convolutional PML was chosen to truncate open boundary of the dispersive waveguide device. The unsplit-field PML was constructed using the split-field PML and the plane-wave solution of electromagnetic field in free space. By applying the convolutional theorem of Fourier transform, the discrete iterative equations of electromagnetic field in the CPML media in the rectangular coordinate system was presented. The performance of CPML was simulated when it was used to truncate the rectangular waveguides excited by the sources with different frequencies and modes. Th