Abstract: To improve the evolution rate and success rate of combination logical circuit,an evolutionary design modeling of circuits using graph-based gene expression programming is presented which combines gene expression with graph structure;the genotype of GGEP is composed of symbols and input connectivity.The genotype can be mapped to a directed acyclic graph that is used to describe a circuit.The optimum circuit has maximum correct outputs with shortest encoding.Mutations take place at non-coding area will have neutral effect refers to selection.The neutral mutation algorithm is proposed and analysis its complexity.The experimental results on two circuits indicated that the proposed approach has a better success rate and convergence rate is 4~20 times faster than other methods.Success rate and convergence rate of evolutionary model with neutral mutations doubled in comparison with non-neutral mutations.