Vibration isolation with mode decoupling plays a crucial role in the design of an intelligent robotic system. Specifically, a coupled multi-degree-of-freedom (multi-DOF) model accurately predicts responses of system dynamics; hence, it is useful for vibration isolation and control with mode decoupling. This study presents a vibration isolation method with mode decoupling based on system identification, including a coupled multi-DOF model to design intelligent robotic systems. Moreover, the entire procedure is described, including the derivation of the governing equation of the coupled multi-DOF model, estimation of the frequency response function, and parameter estimation using least squares approximation. Furthermore, the suggested methods were applied for a mobile surveillance system suffering from resonances with mode coupling; it made the monitoring performance of the surveillance camera deteriorate. The resonance problem was mitigated by installing vibration isolators, but limited to eliminate the coupling effects of natural frequency deterioration performances of vibration isolation. More seriously, system identification with a simple decoupled model limits the prediction of this phenomenon. Hence, it is difficult to enhance the performance of vibration isolators. In contrast, the presented method can accurately predict the vibration phenomenon and plays a critical role in vibration isolation. Therefore, dynamic characteristics were predicted based on a vibration isolator using the coupled three-DOF model, and a final suggestion is presented here. The experiments demonstrated that the suggested configuration decreased vibration up to 98.3%, 94.0%, and 94.5% in the operational frequency range, i.e., 30–85 Hz, compared to the original surveillance system in the fore-after, side-by-side, and vertical directions, respectively. The analysis suggests that the present method and procedure effectively optimize the vibration isolation performances of a drone containing a surveillance system.