In this paper, the research on the initial error compensation of strapdown sea-air gravimeter is carried out. After the gravimeter is turned on, the gravimeter data has a gradually stable process. The error between the unstable value and the stable value in the initial section is estimated, and the error compensation of gravity data is realized. In this paper, the long-term and short-term memory network method is proposed. This method can continuously learn the existing data and predict the future data changes with high accuracy. It is verified that by the measured gravity measurement data that the proposed method has a good error compensation effect, which improves the accuracy and effectiveness of gravity measurement data. The experimental results show that the effect of the measurement error suppression for the initial section of the gravity data is more than 90%, which is of great value for the operation efficiency of the strapdown sea-air gravimeter.