Abstract: Gradient kind methods depend on initial values for reentry trajectory optimization problem.Genetic algorithm requires large population and many iterations for reentry trajectory optimization.In order to avoid the disadvantages mentioned，an improved steady state genetic algorithm combined with successive quadratic programming（GA-SQP）algorithm was proposed.For equal reentry range trajectory design problem，an initial population genic check method was designed.Also a fuzzy fitness function and an inferior gene score method were provided.The reentry overload duration limitation and bank angular velocity limitation were included.In the singularity situations of reentry point behind target point and short brake duration，constraints evaluation method was also provided for successive quadratic programming process.The improved steady state GA-SQP method proposed can be applied to equal reentry range trajectory design in variable orbit altitude situations.The improved steady state  GA-SQP method proposed is independent of initial values.Comparative simulations show that the population and iterations of improved steady state GA-SQP method are decreased.The improved steady-state GA-SQP algorithm needs 34.7% fewer iterations，and its computation speed and result precision are suitable for engineering applications.

Key words: genetic algorithm combined with successive quadratic programming algorithm（GA-SQP）, fuzzy fitness, genic check method, equal reentry range trajectory, reentry orbit, trajectory optimization