We consider a multiple-criterion shortest path problem with resource constraints, in which one needs to find paths between two points in a terrain for the movement of an unmanned combat vehicle (UCV). In the path planning problem considered here, cumulative traverse time of the UCV, risk level, and (communication) jamming level associated with the paths are limited to be less than or equal to given limits. We propose a modified label-correcting algorithm with a new label-selection strategy to find Pareto-optimal solutions for the multiple objectives of minimizing the traverse time, risk level, and jamming level related to the paths. In addition, we develop a path planning algorithm based on the label-correcting method to solve problems with a single objective within a reasonably short time. For evaluation of the performance of the proposed algorithms, computational experiments are performed on a number of instances, and results show that the proposed algorithms perform better than existing methods in terms of a computation time.