In the field of integrated circuit physical design automation, the problem of obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction is a fundamental problem and has attracted a lot of research attention. In this paper, a parallel algorithm for constructing OARSMTs is proposed. The algorithm is based on maze routing and double front-wave expansion. Experimental results show that our algorithm not only generates very short wires, but also performs efficiently on shared-memory multi-core computer systems. Compared with the sequential execution of our parallel program that has been implemented, the program can achieve 23% speed-up on average while running on a multicore workstation.