Abstract: The on-board atomic clock will be affected by such factors as bad space conditions and aging equipment while it is working, so there are often outliers in the satellite clock error data, among which the additive outlier (AO) is a common class of outliers in the clock error sequence. Based on the autoregressive moving average (ARMA) model, this paper proposes an AO detection algorithm, which can not only accurately detect isolated AO, but also accurately detect pieces of AO, and overcome the overwhelming and masking phenomenon that often occurs in other algorithms. When the AO of the clock error sequence is successfully detected, the algorithm can obtain an accurate ARMA model, and then accurately predict satellite clock error. In order to analyze the outlier detection and prediction effect of this algorithm, BeiDou satellite clock error is used to verify it. The results show that the proposed algorithm can accurately detect the AO of the clock error sequence, and has good effects in the short-term prediction of satellite clock errors.