The pulse wave propagation is theoretically investigated in a particular case of a medium of discrete random scatterers. As the basic equation the ordinary space-time transport equation is used under the forward scattering approximation and is solved by means of the eigenfunction method developed in a recent paper. One of the major results is that an explicit expression of pulse intensity is analytically obtained for the realistic scattering amplitude, valid when the size of scatterers is sufficiently large in comparison with the wavelength. The dependence of pulse width broadening on the particle characteristic is also clarified for the case of large optical distances and is compared with that of previous literature. By the same techniques the temporal angular broadening of pulse wave is evaluated in order to find the conditions of applicability of the present method.