For the problem of mobile robot path planning, a path planning method based on quantum-behaved particle swarm optimization(QPSO) algorithm is proposed. The probability theory is applied to study the relationship with the parameters and convergence of mobile robot path planning, and the convergence interval of the method with uniform distribution and normal distribution is clarified. Considering the movement characteristics of mobile robot, an improved trajectory planning method is proposed. Experimental and calculation results show the effectiveness of the proposed method for mobile robot path planning.