In this paper, a model predictive control approach based on a generic particle filter is proposed to synchronize two Josephson junction models with different parameters. For this purpose, an appropriate objective function is defined to assess the particles within the state space. This objective function minimizes simultaneously the tracking error, control effort, and control smoothness. The dynamic optimization problem is solved using a generic particle filter. Here, Josephson junction is described with Resistive Capacitive Inductive Shunted Josephson model, and the synchronization is obtained using the slave–master technique. Moreover, to verify the implementation capability of the proposed algorithm, a processor in loop experiment is performed. The results show that the open-loop system, without the controller, has a chaotic behavior. Numerical simulations are conducted to assess the performance of the proposed algorithm. The results show that the proposed approach can be implemented in a real-time application. Also, the performance of the suggested controller is compared with the proportional integral derivative controller and sliding mode controller.