The high precision satellite clock error prediction is one of the key technical problems for the receiver real-time precision single point positioning technology. To find a rapid and accurate prediction method for small sample satellite clock error sequences, a optimized algorithm model PGM(1, 1) is presented based on the drawback analysis of the conventional GM(1, 1) predication model. The predication model using the latest measurement for initialization is established, followed by replacing the old information with the latest one to realize model predication. In addition, the attenuated memory recursive least squares method is adopted for weighted handling of both the old and new information. The normalized mean relative error is used as accuracy test standard for fitting coefficient optimization factors and particle swarm optimization adaptive optimization is adopted. The typical clock errors error of five GPS satellites are predicted among one day using the PGM(1, 1) model. The prediction accuracy is greatly improved with small training samples compared with the GM(1, 1) model and the second order polynomial model, which indicates that the prediction method can be applied to the accurate and rapid forecasting of satellite clock error.