Due to the growing of multimedia data traffic, the shortest path can not be met the requirements of the future integrated-service. Many researches have proved that multi-paths are useful in telecommunication networks for fault tolerance, increasing bandwidth, and achieving better load balance. In this paper, we proposed an efficient routing algorithm based on the integrated cost of path which is composed of delay cost and diversity cost to find multi-paths with the constraint of diversity threshold and path hops. It changed link cost continuously, and the cost is obtained by normal distribution function. We implemented this algorithm in NSF network topology comparing with edge split algorithm (ESA), and the results show that the proposed algorithm has lower integrated cost.