The problem of finding a minimum-cast multicast tree (Steiner tree) is known as NP complete. Heuristic based algorithms for this problem to achieve good performance are usually time-consuming. In this paper, we propose a new strategy called tree-caching for efficient multicast connection setup in connection-oriented networks. In this scheme, the tree topologies that have been computed are cached in a database of the source nodes. This can reduce the connection establishment time for subsequent connection requests which have some common multicast members, by an efficient reuse of cached trees without having to re-run a multicast routing algorithm for the whole group. This method can provide an efficient way to eliminate, when ever possible, the expensive tree computation algorithm that has to be performed in setting up a multicast connection. We first formulate the problem of tree-caching and then propose a tree-caching algorithm to reduce the complexity of the tree computations when a new connection is to be established. Through simulations, we find that the proposed tree-caching strategy performs very well and can significantly reduce the computation complexity for setting up multicast connections.