Over past decades, although many none based-gradient optimization algorithms have been used for the design of mechanisms. In synthesis of mechanisms, designing mechanism with giving the output motion, a path of point, is still a challenge. This work presents a new algorithm, named the combination of differential evolution and Jaya algorithm (CDEJ) for calculating the kinematic dimensions of four-bar mechanisms. In this paper, the CDEJ method is used in the dimensional design of the four-bar linkage in order to satisfy the path of couple point. The results of the proposed method are compared to classical methods e.g., the differential evolution and Jaya methods. The results shows that the CDEJ method has a better performance in terms of accuracy of solutions and saves time for achieving the optimal solution.