A novel navigation algorithm using a tree search procedure developed in Artificial Intelligence has been proposed for both the air-toair combat between fighter planes and the approach of missiles to air-targets. This algorithm is much easier with respect to the mathematical treatment of the nonlinearity of system equations and the boundary conditions than the differential game method. And it takes much more account of the reciprocal action between a pursuer and a evader than the usual navigation algorithm such as proportional navigation, pure pursuit and so on, by means of AND/OR game tree search which is much more efficient than the pure minimax procedure. This paper presents a comparison between the navigation algorithm using the game tree and the pure pursuit which is often adopted especially in air-to-air combat simulation models, and shows a difference between the shallow tree search navigation algorithm and the deep one, by use of a very simple air-to-air combat model.