This paper proposes a new distributed shortest path (SP) based delay constrained multicast routing algorithm which is capable of constructing a delay constrained multicast tree when node failures occur during the tree construction period and recovering from any node failure in a multicast tree during the on-going multicast session without interrupting the running traffic on the unaffected portion of the tree. The proposed algorithm performs the failure recovery efficiently, which gives better performance in terms of the number of exchanged messages and the convergence time than the existing distributed SP-based delay constrained multicast routing algorithms in a network where node failures occur.