The safe and reliable operation of transformer plays a crucial role in power system. In case of the oil-immersed transformer, considering the fault characteristics and data monitoring situation of transformer, the solubility of five main fault characteristic gases, which are critical elements in IEC three ratio codes, is predicted to provide the basis for data analysis for the subsequent fault diagnosis. For incomplete and small sample characteristics of gas concentration data acquisition in gas chromatographic analysis of transformer faults, the unequal interval GM (1,1) power prediction models of gas solubility of different gases are established respectively. The coordinated optimization for background value and power exponent based on genetic algorithm is applied. According to the experiment, the proposed method can effectively improve the fitting and prediction accuracy, and the model has no limit to the equidistant coherence of the basic data, with better practicality and adaptability, when compared to some existing in the literature, such as the GM (1,1) model and Verhulst model. This work is supported by Sino-US International Science and Technology Cooperation Project (No. 2016YFE0105300).