This work presents an overlay multicast tree construction algorithm to support stable multimedia service over the Internet. While constructing a multicast tree, it takes into account not only the link delay, but also the peer stability. Since peers actually show dynamic and unstable behavior over peer-to-peer network, it is essential to consider the peer stability. Furthermore, the weighting factor between link delay and peer stability is adaptively controlled. Basically, Genetic algorithm is employed to obtain a near optimal solution with a low computational complexity. Finally, simulation results are provided to show the performance of the proposed algorithm.