Based on the problem of considering the link cost into delay constraint, this paper proposes a new delay constrained minimum cost path algorithm (DCMC) which is used for searching the shortest path between nodes. On this basis, an efficient center node selection method is further modified based on the cost-delay ratio (CDR). Based on application of CBT a center selection for delay constrained minimum cost multicast routing (CS_DCMCMR) algorithm is proposed by using the above two algorithms. In the use of this algorithm, both cost and delay are taken into consideration simultaneously in path search and central node selection. The simulation results show that the time complexity of CS_DCMCMR algorithm is O(mlogn), compared with CSDVC and CCLDA algorithms, the use of this algorithm can largely reduce the total cost of the final multicast tree in the case of meeting delay and delay variation constraints without the increase of complexity.