Multiple dynamic supply voltage (MDSV) provides an effective way to reduce dynamic power and is widely used in high-end or low-power designs. The challenge of routing MDSV designs is that the net in MDSV designs needs to be planned carefully to avoid electrical problems or functional failure as a long interconnect path pass through the shutdown power domains. As the first work to address the MDSV global routing problem, power domain-aware routing (PDR) problem is defined and the point-to-point PDR algorithm is also presented herein with look-ahead path selection method and look-up table acceleration approach. For multi-pin net routings, a novel constant-time table-lookup mechanism by invoking four enhanced monotonic routings to fast compute the least-cost monotonic path from every node to the target sub-tree is presented to speed up the query about routing cost (including driven-length slack) to target during multi-source multi-target PDR. Experimental results confirm that the proposed MDSV-based global router can efficiently identify legally optimized routing results for MDSV designs, and can effectively reduce overflow, wire length, inserted level shifters and runtime.