Focusing on a particular assembly line balancing problem of which the task time is a stochastic variable, a stochastic model is established, which aimed at maximization of assembly line balancing rate, completed probability and smoothness index. Simultaneously, an improved particle swarm optimization algorithm is proposed to solve this problem and a reasonable chromosome coding method which effectively prevent to generate infeasible solution is designed. For this reason, the algorithm convergence rate could be improved. At last, rear axle assembly line balancing designs of an automotive part company is taken to test validity of algorithm. Availability of the algorithm is verified by this example.