This paper proposes a dominant source-based tree (DSBT) that constructs a localized multicast routing tree for dynamic multicasting without rerouting. To constrain end-to-end delays a multicast tree needs to be reconstructed when a new node joins the group due to additive tree constraint. In DSBT, a multicast group G is expressed by a (DS, NCM) pair, where DS is a dominant source address and NCM is a normalized cost margin. A node wishing to participate in a group selects a path that complies with NCM toward DS such that the end-to-end cost is constrained without any rerouting. Simulation results show that the proposed method performed better in terms of the overall tree cost compared with the Nave algorithm and in terms of the end-to-end delays between any two members compared with the Greedy algorithm.