The critical problem for multicasting is to find optimal multicast tree. Most popular multicast algorithms over WAN are usually based on either Dijkstra?s shortest path tree or Steiner tree, which assume that sender can send a message to the next destination node right away. This can lead to a non-optimal multicast tree as it ignores gap parameter in LogP model. From our preliminary study, we found that gap is very significant especially in WAN. In this paper, we take gap into consideration and propose a minimization technique, which apply gap parameters to Dijkstra?s shortest path algorithm to construct minimized shortest path trees. We compare the multicast latency of normal Dijkstra?s shortest path multicast tree and our minimized multicast tree with simulation. The results show that multicast tree based on our proposed algorithm can clearly out-perform the multicast tree based on Dijkstra?s algorithm. Our results further indicate that our proposed algorithm can perform very well when message size is large with lots of nodes.