Aiming at the synthesis of space sparse arrays with constraints on array aperture, array spacing and number of arrays, a Lévy flight Particle Swarm Optimization(PSO) is proposed. The Lévy flight PSO is introduced to increase the particle position of the population, avoiding the algorithm falling into the local optima and renewing unsolvable. Simulation results show that the Lévy flight PSO has better convergence accuracy than the genetic algorithm and PSO in the literatures, which verifies the effectiveness and robustness of the proposed algorithm.