We consider a problem of finding a reconnaissance route of an unmanned combat vehicle (UCV) in a terrain, which is modeled as a grid. It is assumed that the traverse time to pass through each cell in the grid and risk level associated with each cell are given and that the cells where the reconnaissance points to be visited by the UCV are located and the visiting sequence of such cells are given in advance as in real situation of military operation. We focus on the problem with the objective of minimizing the total travel time of the UCV for a given limit on the sum of risk level values associated with the cells on the path of the UCV. We develop an optimal solution algorithm based on a dynamic programming algorithm for multiple-choice knapsack problems. We also present a heuristic algorithm, which can be used for large-size problems. For evaluation of the performance of the proposed algorithms, computational experiments are performed on a number of problem instances, and results show that the proposed algorithms give optimal or good solutions within an acceptable time for real military operations.