The distributed sub-tree (DST) scheme in the elastic optical datacenter network (EODN) can use multiple datacenters (DCs) to jointly serve a multicast request. By allocating some suitable DCs to the multicast request, the route length can be reduced, thereby reducing resource consumption and decreasing blocking probability. However, DST scheme also has a defect that, all source nodes of multicast requests are hosted in the DCs, which leads to that links connecting the DCs nodes have higher usage than other links, and the resulting network bottleneck makes the network performance declines sharply. In this paper, we propose a link-aware cost calculation (LA-CC) formula and a link-aware distributed steiner sub-tree (LA-DSST) algorithm to make the usage of all links as balanced as possible, thus reducing the blocking probability caused by network bottlenecks. Simulation results show that our proposed algorithm significantly improves performance with the lowest blocking probability compared to existing well-performing algorithms.