In this paper, a discrete particle swarm optimization (PSO) algorithm called DPSO is proposed to solve the two-stage assembly scheduling problem with respect to bicriteria of makespan and mean completion time where setup times are treated as separate from processing times. In DPSO, the particle velocity representation is redefined, and particle movement is modified accordingly. In order to refrain from the shortcoming of premature convergence, individual intensity is defined, which is used to control adaptive mutation of the particle, and mutation mode is decided by the individual fitness. Furthermore, a randomized exchange neighborhood search is introduced to enhance the local search ability of the particle and increase the convergence speed. Finally, the proposed algorithm is tested on different scale problems and compared with the proposed efficient algorithms in the literature recently. The results show that DPSO is an effective and efficient for assembly scheduling problem.