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In todaypsilas VLSI designs, there can be many blockages in a routing region. The obstacle-avoiding rectilinear Steiner minimum tree (OARSMT) problem has become an important problem in the physical design stage of VLSI circuits. This problem has attracted a lot of attentions in research and several approaches have been proposed to solve this problem effectively. In this paper, we will present a heuristic maze routing based approach to solve this OARSMT problem. It is commonly believed that maze routing based approaches can only handle small scale problems and there is a lack of an effective multi-terminal variant to handle multi-pin nets in practice. We will show in this paper that maze routing based approaches can also handle large scale OARSMT problems effectively. Our approach is based on the searching process as in maze routing and can handle multi-pin nets very well in both solution quality, running time and memory space usage. We have compared our results with those of the previous works and can show that we can out-perform the best previous results on this problem  by giving an OARSMT with 2.01% less wire length on average and can make a 27.04% improvement in wire length in comparison with a lower bound of the optimal solution on average, while the running times are all very short and comparable to those in . Besides, due to the flexibility of maze routing, we can handle different kinds of obstacles with different convex or concave rectilinear shapes directly without a need to partition each blockage into a set of rectangular sub-blockages, which will increase the size of the problem.