Abstract: To solve the problem of quantum particle swarm optimization algorithm appears the poor diversity of population at the end of iteration, three improvements are proposed:(1) associating the contraction-expansion coefficient with the fitness value, the contraction-expansion coefficient will adjust adaptively with the change of the fitness value of the particle; (2) differential strategy is used to update the random location of particles which makes the particle approach the optimal position of the population; . (3) updating particle position with Levy flight strategy, Levy flight strategy's occasional long jumps are utilized to increase the diversity of population and the ability of jump out of the local optimum. A hybrid adaptive quantum particle swarm optimization (HAQPSO) algorithm is proposed based on the above three points. By comparing the simulation result of 6 typical functions shows that:Improved quantum particle swarm optimization algorithm has better global convergence ability than the quantum particle swarm optimization algorithm, and the convergence precision, speed and stability are improved obviously.