The propagation of the high power electromagnetic pulse has been numerically simulated in the whole ionosphere. Using the shortened ionosphere profile, the equations of high power electromagnetic pulse propagating in the cold plasma could describe the high power electromagnetic pulse propagating in the ionosphere. The perfect match layer(PML) boundary condition was adopted. The finite difference time domain(FDTD) method for solving this problem would waste great time and memory. Therefore, the pseudospectral time-domain(PSTD) method was used to solve the equations of cold plasma. The data of propagation of the high power electromagnetic pulse in the whole ionosphere acquired by this method accords with the result of (FD)2TD numerical modeling, which demonstrates the validity of PSTD algori