With the increasing energy costs and the serious environmental issue, peak power consumption attracts much attention by manufacturing industries. It requires that the real-time power consumption cannot exceed a given peak power at any time during manufacturing process. Aiming at the permutation flowshop scheduling problem with peak power consumption constraint (PFSPP), a cooperative memetic algorithm is proposed. First, multiple decoding methods are collaborated to generate diverse and feasible schedules, and a heuristic and random method are fused to initialize population. Second, two problem-specific search operators are designed according to the characteristics of the problem for adjusting the job sequence and speed selection, respectively. Furthermore, according to distribution of individuals in the objective space, a cooperation scheme is designed. Different search operators are used for the individuals in different regions. In addition, a local intensification is performed on the elite individual to further improve the performance. Numerical tests are conducted by using extensive instances. Finally, the effectiveness of the designed cooperation mechanisms is demonstrated. Moreover, the comparisons with the math solver and the existing algorithms show that the proposed algorithm is more effective in solving the PFSPP.