Abstract: The optimum searching problem, in which beyond-line-of-sight missile flying in the terminal of midcourse guidance searches the moving target automatically to maximize the probability of acquisition by use of the residual propellent was studied. The position-probability distribution of moving target was provided. The project of searching course-line based on the position-probability distribution was proposed. The composition schema of the searching system was drawn up and the system was designed. At last, the system was simulated and the probability of acquisition of moving target was proved.