The problem of computing delay-constrained minimum-cost multicast trees is of great interest in the last few years. So far, the Bounded Shortest Multicast Algorithm (BSMA) has been thought to be the best constrained multicast algorithm. However, the large computation time restricts its application. As a global optimizing algorithm, Genetic algorithm (GA) is applied to solve the problem of multicast more and more. GA has more powerful searching ability than traditional algorithm, however, the property of "prematurity" makes it difficult to get a good multicast tree. A Clonal Strategies (CS) based multicast algorithm is presented in this paper, which saliently solves the "prematurity" problem in Genetic based multicast algorithm. Furthermore, the algorithm is accelerated by using an adjustable parameter to reduce the search space. The algorithm has the property of simple realization and flexible control. The simulated results show that CS has better performance than BSMA and GA.