We have developed and evaluated an efficient heuristic algorithm to construct a multicast tree with the minimum cost. Our algorithm uses multiple candidate paths to select a path from source to each destination, and works on directed asymmetric networks. We also show that our proposed algorithm have a perform gain in terms of tree cost for real life networks over existing algorithm. The time complexity of our algorithm is O( D (m + nlogn) ) for a m-arc n-node network with D number of members in the multicast group, and is comparable to well-known algorithm, TM [13], for a multicast tree construction in terms of the time-complexity. We have performed empirical evaluation that compares our algorithms with the others on large networks.