Based on the analysis of particle swarm optimization algorithm, the particle is described in the quantum space and the potential energy field model is created. And then according to the swarms gregariousness, the quantum-behaved particle swarm optimization (QPSO) algorithm is derived. Within the framework of random algorithms global convergence theorem, the convergence of QPSO algorithm is discussed and is proved to be a kind of global convergence algorithm. Three kinds of control strategy are proposed for the unique parameter of QPSO algorithm and they are tested on five benchmark functions. According to the test results, some conclusions concerning the selection of the parameter are drawn.