The minimum rectilinear Steiner tree (MRST) problem is an NP-complete problem which arises in VLSI wiring,network routing and many combinatorial optimization problems.In this paper,an O(n²) time complexity approximation algorithm for MRST is proposed.The approximation ratio of the algorithm is strictly less than 3/2.The computer verification of the algorithm shows that the costs of the produced spanning trees are only 0.8% away from the optimal.In addition,this algorithm can be revised for multidimensional Manhattan space and implemented in parallel/distributed environments easily.