The Steiner minimal tree problem in graphs(GSTP) is a well known NP hard problem.Its applications can be found in many areas,such as telecommunication network design,VLSI design,etc.A competitive decision algorithm was developed to solve the GSTP.The mathematical properties of GSTP were analysed,which can be used to scale down the size of original problem and accelerate the algorithm.To assess the efficiency of the proposed competitive decision algorithm,it was applied to a set of benchmark problems in the OR Library.In terms of computation times,our algorithm clearly outperforms other heuristics for the Steiner problem in graphs,while obtaining better or comparable solutions.