According to Kirchhoffs approximation，the fourth order moment statistical characteristic of the pulsed wave scattering by random rough surfaces is investigated numerically. As a special application，the fourth order moment （FOM） is simplified to obtain mutual correlation functions of the the two positions and two frequencies of pulsed wave scattering by random rough surface. It is found that the distributions of FOM vary with the coherence bandwidth frequency difference and scattering angle for different incidence angles. The numerical results show that the mean of fluctuating heights and coherent length of random rough surfaces have also an important influence on FOM. Generally，the largest scattering value and smallest coherence bandwidth of the FOM occur at the specific directions. That is to say，the FOM will have a lower coherent component and its distributions of scattering angles will be broadened in relation to the rugged surface. Meanwhile，the FOM decreases rapidly when there is a bigger coherence bandwidth frequency difference.