The electricity market is particularly complex due to the different arrangements and structures of its participants. If the energy price in this market presents in a conceptual and well-known way, the complexity of the market will be greatly reduced. Drastic changes in the supply and demand markets are a challenge for electricity prices (EPs), which necessitates the short-term forecasting of EPs. In this study, two restructured power systems are considered, and the EPs of these systems are entirely and accurately predicted using a Gaussian process (GP) model that is adapted for time series predictions. In this modeling, various models of the GP, including dynamic, static, direct, and indirect, as well as their mixture models, are used and investigated. The effectiveness and accuracy of these models are compared using appropriate evaluation indicators. The results show that the combinations of the GP models have lower errors than individual models, and the dynamic indirect GP was chosen as the best model.