An important issue for providing better guarantees of Quality of Service (QoS) to applications is QoS rout-ing. The task of QoS routing is to determine a feasible path that satisfies a set of constraints while maintaining high u-tilization of network resources. For the purpose of achieving the latter objective additional optimality requirementsneed to be imposed. In general, multi-constrained path selection problem is NP-hard so it cannot be exactly solved inpolynomial time. Accordingly heuristics and approximation algorithms with polynomial or pseudo-polynomial timecomplexity are often used to deal with this problem. However, many of these algorithms suffer from either excessivecomputational complexity that cannot be used for online network operation or low performance. Moreover, they gen-erally deal with special cases of the problem (e. g. , two constraints without optimization, one constraint with opti-mization, etc. ). In this paper, the authors propose a new efficient algorithm (EAMCOP) for the problem. Makinguse of efficient pruning policy, the algorithm reduces greatly the size of search space and improves the computationalperformance. Although the proposed algorithm has exponential time complexity in the worst case, it can get verygood performance in real networks. The reason is that when the scale of network increases, EAMCOP controls effi-ciently the size of search space by constraint conditions and prior queue that improves computational efficiency. Theresults of simulation show that the algorithm has good performance and can solve effectively multi-constrained opti-mal path (MCOP) problem.