In this paper', the methodology of generating an optimal trajectory on a complex terrain for a specific vehicle is proposed. The possible paths are constrained by the Limitations on the terrain and the capability of the vehicle. To deal with these constraints, the notions of forbidden paint, forbidden direction, and forbidden path are introduced. After certain constants are specified, the method of dynamic programming is then invoked to find the optimal solution. If the target is beyond the maximal range of the vehicle, appropriate senice stations are selected by using the auction algorithm To speed up the computation process, the ideas of bi-spiral scheme and instant update are employed. With all the techniques at hand, numerical results show that the proposed method can generate the desired bajectory eiTiciently.