Selecting the minimum primer set with multiple constraints is an effective method for a successful and economical Multiplex Polymerase Chain Reaction (MP-PCR) experiment. However, there is no suitable algorithm for solving the problem. In this paper, a mathematical model is presented for the minimum primer set selection problem with multiple constraints. By introducing a novel genetic operator, we developed a parthenogenetic algorithm MG-PGA to solve the model. Experimental results show that MG-PGA can not only find a small primer set, but can also satisfy multiple biological constraints. Therefore, MG-PGA is a practical solution for MP-PCR primer design.