In view of the slowness and the locality of convergence for Simple Genetic Algorithm(SGA for short) in solving complex optimization problems,we propose an improved genetic algorithm named multi-stage composite genetic algorithm (MSC-GA for short) by reducing the optimization-search range gradually,and give the structure and the implementation steps of MSC-GA;then we consider its global convergence under the elitist preserving strategy using Markov chain theory,and analyze its performance through three examples from different aspects.All these indicate that the new algorithm possess interesting advantages such as better convergence,less chance trapping into premature states,which can be widely used in many large-scale and high-accuracy optimization problems.