A "decomposition-reconstruction-prediction" satellite clock offset prediction method based on singular spectrum analysis (SSA) is proposed. This method first decomposes the clock offset time series into trend, periodic, and random signals. Then, based on the significant difference in Hurst exponent among the three types of signals, the reconstructed clock offset signal is determined. Finally, the SSA iterative interpolation algorithm is used to extrapolate the reconstructed clock offset signal and obtain the final predicted clock offset time series. Taking GPS and BDS-3 satellite clock offsets as an example, the results show that SSA can accurately extract trend and periodic signals in clock offset time series. Compared to the quadratic polynomial model with periodic term, grey model and autoregressive integrated moving average model, the proposed method has a smaller root mean square error in prediction and more stable prediction results. For the 12-hour prediction, the average prediction accuracy of GPS satellite clock offset is improved by 38.81%, 59%, and 72.11% compared to the other three models, respectively, while the accuracy of BDS-3 satellite clock offset is improved by 71.54%, 74.82%, and 70.09%, respectively. For the 24-hour prediction, the improvements for GPS satellite clock offset are 51%, 70.66%, and 83.99%, respectively, while the improvements for BDS-3 satellite clock offset are 86.36%, 85.25%, and 81.05%, respectively. It is concluded that the proposed method is effective and practical for satellite clock offset prediction.