This paper proposes a novel quantum genetic algorithm (QGA)——PSQGA

which uses particle swarm optimization method instead of quantum gate to update the state of quantum bit.It has the advantages of particle swarm optimization and quantum genetic algorithm.A variance function is introduced to estimate the stability of the algorithm.Though the experiments of four continuous functions and combination optimization problems

as well as its application to image sparse decomposition.Compared with the improved algorithm which involved quantum gate (IQGA)

the ability of finding the best solution and the stability of PSQGA are greatly improved.PSQGA has better convergent property and ability of searching more extensive space.It is fit for the solution of complex optimization problems.