The precision, stability, and bandwidth of accelerometers are vital for inertial navigation and motion control. This study proposes a quantum-classical hybrid accelerometer that integrates a cold atom interferometer (CAI) with a quartz flexible accelerometer (QFA) using an optimized extended Kalman filter algorithm. High-fidelity numerical simulations based on Markov Chain Monte Carlo methods are conducted to model the sensors' intrinsic noise and environmental vibration under shipborne conditions. A novel vibration-compensation scheme is introduced to stabilize the CAI output through precise control of the Raman laser phase. Simulation results demonstrate that the hybrid system achieves high-precision, high-bandwidth acceleration measurements in dynamic scenarios, effectively eliminating the long-term drift inherent in classical sensors. Performance analysis via Allan deviation and noise power spectral density confirms that long-term instability is suppressed. As for normal sailing, the Kalman filter successfully tracks and corrects up to 91.62% of the QFA measurement errors, while low-pass filtering further mitigates errors induced by vibration noise. Furthermore, the system exhibits excellent robustness during extreme acceleration events, such as ship collisions. This work provides a comprehensive simulation framework for hybrid quantum-classical accelerometers and highlights their potential for high-dynamic inertial navigation applications.