Abstract: Aiming at features of the Markowitz mean-variance model and the weakness and shortage of simple Genetic Algorithm(GA) in the model,a kind of improved GA,namely dual mutation GA,is put forward.This algorithm introduces the mutant operator in the crossover operator,that is,a great quantity of close relation individuals appear in population,inbreeding is produced,crossover is stopped to mutate uniformly;In the meantime,the mutation operator is brought in the gradient direction to accelerate the algorithm convergence speed.The numerical experiment demonstrates that dual mutation algorithm presents features of global convergence,fast speed and avoiding of prematurity in solving the Markowitz mean-variance model.