A single-parent genetic algorithm (SPGA) is developed from the traditional genetic algorithm to optimize cluster structures. Two mutation operators are used to find the global minimum on the potential surface. The algorithm for optimizing the structure of molecule clusters is proposed. Combined with the TIP3P potential energy, the structures of water clusters (H2O)n(n≤14) is studied using SPGA. The stable structures obtained are in complete agreement with the reported results obtained theoretically and experimentally. The calculation results show that SPGA is an efficient and reliable method to find the global minimum structure of molecular clusters.