Steiner Minimal Tree (SMT) is a complex optimization problem that has many important applications in science and technology; This is a NP-hard problem. Much research has been carried out to solve the SMT problem using approximate algorithms. This paper presents A Variable Neighborhood Search (VNS) algorithm for solving the SMT problem in sparse graphs; The proposed algorithm has been tested on sparse graphs in a standardized experimental data system, and it yields better results than some other heuristic algorithms.