Within the current energy structure in China, coal consumption accounts for 60% of the total energy consumption. Understanding the features of coal prices is important to the energy industry as the prices have a profound impact on the energy development, especially to the thermal power business. This paper uses the multi-fractal theory introduced from financial price field to examine the fluctuations of thermal power coal price by multi-fractal detrended fluctuation analysis (MFDFA). A steam coal Free-on-Board (FOB) price in Qinhuangdao Port, China's largest port of coal storage and transportation, was chosen to represent the thermal power coal price and to reflect the price fluctuation. The analysis shows that the thermal power coal price has multi-fractal features. Consequently, a Quarterly Fluctuation Index (QFI) for thermal power coal price was proposed to forecast the coal price caused by market fluctuation as the fractal model based on QFI had a better forecasting ability when the prices fluctuate wildly. Especially, the QFI can help both government and enterprises to improve their capabilities to manage the fluctuation risks. This study also provides a useful reference to understand the multi-fractal fluctuation features in other energy prices.