Measurement of liquid level in vessels under ocean conditions, such as in the marine nuclear reactor pressure vessel, pressurizer and so on, suffers from the problem of strong free surface distortion. In order to solve such problem, an online prediction method based on reduced order model (ROM) and compressive sensing theory is proposed in this paper. The whole field online prediction of complex fluid flow characteristics can be realized by combining the observation data from the known sparse sensor with the ROM. In this paper, the three-dimensional flow field of sloshing flow in a cavity is numerically simulated to establish abundant numerical database. Taking the liquid level of the flow field as the prediction object, the ROM is established by using the proper orthogonal decomposition (POD) method to predict the liquid level. The results show that POD ROM can accurately predict the unknown case, the smaller the rotating speed is, the better the prediction result is, and increasing the number of measuring points and the number of basis functions can reduce the prediction error to a certain extent. The reduced model constructed by using QR decomposition to obtain measuring points can effectively reduce the error of prediction results.