The day-ahead electricity market is closely related to other commodity markets such as the fuel and emission markets and is increasingly playing a significant role in human life. Thus, in the electricity markets, accurate electricity price forecasting plays significant role for power producers and consumers. Although many studies developing and proposing highly accurate forecasting models exist in the literature, there have been few investigations on improving the forecasting effectiveness of electricity price from the perspective of reducing the volatility of data with satisfactory accuracy. Based on reducing the volatility of the electricity price and the forecasting nature of the radial basis function network (RBFN), this paper successfully develops a two-stage model to forecast the day-ahead electricity price, of which the first stage is particle swarm optimization (PSO)-core mapping (CM) with self-organizing-map and fuzzy set (PCMwSF), and the second stage is selection rule (SR). The PCMwSF stage applies CM, fuzzy set and optimized weights to obtain the future price, and the SR stage is inspired by the forecasting nature of RBFN and effectively selects the best forecast during the test period. The proposed model, i.e., CM-PCMwSF-SR, not only overcomes the difficulty of reducing the high volatility of the electricity price but also leads to a superior forecasting effectiveness than benchmarks.