In order to overcome the problems of low convergence precision and easily relapsing into local optimum in Fruit fly Optimization Algorithm (FOA), by introducing the Levy flight strategy into the FOA, an improved FOA called double subgroups FOA with the characteristics of Levy flight (LFOA) was proposed. Firstly, the fruit fly group was dynamically divided into two subgroups (advanced subgroup and drawback subgroup) whose centers separately were the best individual and the worst individual in contemporary group according to its own evolutionary level. Secondly, a global search was made for drawback subgroup with the guidance of the best individual, and a finely local search was made for advanced subgroup by doing Levy flight around the best individual, so that not only both the global and local search ability balanced, but also the occasionally long distance jump of Levy flight could be used to help the fruit fly jump out of local optimum. Finally, two subgroups exchange information by updating the overall optimum and recombining the subgroups. The experiment results of 6 typical functions show that the new method has the advantages of better global searching ability, faster convergence and more precise convergence.