As Satellite Clock Bias (SCB) prediction may be affected by various factors such as periodic items, sampling length, and stochastic items, a fusion-based prediction method is proposed by considering characteristics of SCB and fitted residue. On this basis, an instance algorithm is presented by fusing four typical prediction models. First, we use Empirical Mode Decomposition (EMD) to pre-process and decompose the SCB series into multiple components with various characteristics. Then, we analyse the fitting performance of each model for different components and prediction length, namely short-, mid- and long-term prediction, and select models with the best performance. Next, we analyse fitted residue of the reconstructed SCB, and select the model with the best fitting results. Finally, we fuse the multiple selected models for SCB prediction. The method is tested using Global Positioning System (GPS) precise clock products provided by the International Global Navigation Satellite System Service (IGS). Experimental results show that, compared with single prediction models and existing combination models, the proposed fusion-based prediction method improves accuracy and stability. In particular, the proposed method is more stable and has better performance for mid- and long-term prediction.