In this paper, we have discussed the synchronization between coupled Josephson Junctions which experience different chaotic oscillations. Due to potential high-frequency applications, the shunted nonlinear resistive-capacitive-inductance junction (RCLSJ) model of Josephson junction was considered in this paper. In order to obtain the synchronization, an adaptive MIMO controller is developed to drive the states of the slave chaotic junction to follow the states of the master chaotic junction. The developed controller has two parts: the fuzzy neural controller and the sliding mode controller. The fuzzy neural controller employs a fuzzy neural network to simulate the behavior of the ideal feedback linearization controller, while the sliding mode controller is used to ensure the robustness of the controlled system and reduce the undesired effects of the estimate errors. In addition, the Lyapunov candidate function is also given for further stability analysis. The numerical simulations are carried out to verify the validity of the proposed control approach. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.