The heatsink can greatly improve the heat dissipation capacity and thermal safety of power devices. However, for practical engineering, the cost of heatsink should be strictly controlled, otherwise it will seriously affect the economy of the whole electronic power device. Therefore, a cost-minimization method for heatsink of power devices based on thermal constraints was proposed in this paper. With the thermal network model of power devices, the maximum junction temperature and thermal time constant were used as thermal safety constraints and the best parameters of heatsink mass and heat dissipation area were found by nonlinear optimization algorithm so as to achieve the optimization goal of the lowest heatsink cost. Taking power Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) and several heatsinks as examples, the results show that the proposed method can provide an important basis for reasonable design or selection of heatsinks.