The spatial-temporal distribution of underwater sound velocity affects the propagation mode of underwater acoustic signals. Therefore, rapid estimation and prediction of underwater sound velocity distribution is crucial for providing underwater positioning, navigation and timing (PNT) services. Currently, sound speed profile (SSP) inversion methods have a faster time response rate compared to direct measurement methods, however, most SSP inversion methods focus on constructing spatial dimensional sound velocity fields and are highly dependent on sonar observation data, thus high requirements have been placed on observation data sources. To explore the distribution pattern of sound velocity in the time dimension and achieve future SSP prediction without sonar observation data, we propose a hierarchical long short-term memory (H-LSTM) neural network for SSP prediction. By our SSP prediction method, the sound speed distribution could be estimated without any on-site data measurement process, so that the time efficiency could be greatly improved. Through comparing with other state-of-the-art methods, H-LSTM has better accuracy performance on prediction of monthly average sound velocity distribution, which is less than 1 m/s in different depth layers.