According to the characteristics of swaying data of spacecraft tracking, telemetering and control ships, a filtering and prediction method, based on a “current” statistical Jounce model model, and the maximum correntropy Kalman filter is proposed. Based on the analysis of the periodic characteristics of ship swaying data, the data noise is analyzed by using frequency domain filtering methods, and it is a non-Gaussian white noise. It is pointed out that the fourth order difference of the ship swaying data is significantly weakened periodically. To tackle the complication of ship rocking dynamics modeling, the maneuvering target tracking theory is introduced. In view of the problem that the current model order is not high enough, the CS-Jounce model is derived based on the “current” statistics. Aiming at the problem of nonGaussian white noise of shipswaying data, the maximum correntropy Kalman filter is introduced. The experimental results based on actual data show that the proposed method can track the shipswaying data well. The filtering accuracy is high and the mean square error of the three step prediction is less than 5 seconds of arc. Meanwhile, the proposed method can accurately estimate and predict the ship's angular velocity and angular acceleration.