According to the characteristics of perfectly matched layers (PML), a convolutional PML (CPML) is chosen to truncate open boundaries used in the numerical simulation of low-altitude electromagnetic pulse. On the basis of the split-field PML and the plane-wave solution of electromagnetic field in a free space, an unsplit-field PML is constructed. With convolutional theorem in the Fourier transformation, discerete iterative equations of electromagnetic field components in the CPML media are presented in three-dimensional prolate-spheroidal coordinate system. The effectiveness of the method in numerical simulation of nuclear electromagnetic pulse is shown.