Wind energy does not produce air or water pollution during its generation and is one of the fastest-growing energy sources worldwide. As a result, the demand for efficient wind turbine operation is increasing, and the condition of the gearbox significantly affects the operation of the entire wind turbine. In this article, we propose using extension theory for the fault identification of the gearbox. Owing to the characteristics of extension sets, where the feature values range from −∞ to +∞, compared with fuzzy sets with values ranging from 0 to 1, extension sets are more convenient than fuzzy sets for quantifying feature values. Therefore, we selected extension theory as the basis for the experiment. For subsequent analysis, a model with four gears and a low speed-to-high speed ratio of 1:12.25 was constructed on the basis of the structure of large wind turbines. A servo motor was used to simulate the operation driven by wind-transmitted energy, and an NI-9234 high-speed acquisition card, along with a three-axis vibration sensor, was used to collect the generated data. The collected vibration signals were processed using fast Fourier transform to reduce unnecessary noise. The signals were categorized into different range intervals on the basis of vibration amplitude, and the occurrences of each interval were used as features for classification. Matrix Laboratory was employed to calculate the correlation function values to determine the fault types. Experimental results showed that the proposed method achieved a recognition success rate of 94.625% for four different types of gearbox. Thus, by this method, we effectively classified gearboxes and achieved the goal of gearbox fault diagnosis.