Abstract: By taking the numerical method and traffic phenomena into account, reasonable improvement is attained on the kinetics equation of the L-W theory. The comparison between what is deduced from the original model by means of characteristics and discontinuity analysis and what is shown by the numerical results of the improved model is made, which further reveals that the latter is the approximation of the former and that such results are convincing. Numerical examples include such problems as red-and-green and traffic accidents, which concern mixed density distribution from the minimum to the maximum, lane changing and a quick density increase or decrease on the boundary and which are also considered most challenging in the field.