In this paper, a new objective function named circular proximity function (CPF) is proposed for the synthesis of four-bar motion generator linkages. This function is designed to measure the similarity of a group of points in Cartesian space to a circular curve. This function lowers the number of optimization variables to only two variables reducing the computational cost significantly. The optimization process has been carried out by the method of Differential Evolution (DE). Four case studies have been investigated in this study to demonstrate the advantages and disadvantages of the proposed method.