In order to solve the problem of truncating the open boundaries of cylindrical waveguides used in the simulation of high-power microwave (HPM) sources, this paper studies the convolutional perfectly matched layer (CPML) in the cylindrical coordinate system. The electromagnetic field's finite-difference time-domain (FDTD) equations and the expressions of axis boundary conditions are presented. Numerical experiments are conducted to validate the equations and axis boundary conditions. The performance of CPML is simulated when it is used to truncate the cylindrical waveguide excited by the sources with different frequencies and modes in the two-and-a-half-dimensional (2.5-D) problems. Numerical results show that the maximum relative error is less than -95 dB, and demonstrate that the property of CPML is much better than that of the Mur-type absorbing boundary condition when they are used to truncate the open boundaries of waveguides. The CPML is especially suitable for truncating the open boundaries of the dispersive waveguide devices in the simulation of HPM sources