The problem of finding a path with two additive constraints is called a multi-constrained path (MCP) problem in the literature. In this paper, we explore the MCP problem based on the idea of single mixed weight. Given two infeasible paths, it can be theoretically proved that a better path can possibly be found if we choose an appropriate parameter to construct the mixed weight. An approximate algorithm is thus proposed to solve the MCP problem. A large number of experiments on networks of different sizes demonstrate that this algorithm can make a correct judgment whether there is a feasible path or not with a very high probability. On the other hand, the time complexity of this algorithm is very small since it only needs to execute Dijkstra's algorithm a limited number of times even for a network of relatively large size.