Wind-powered electricity generation has grown significantly over the past decade. While there are many components that might impact their useful life, the gearbox and generator bearings are among the most fragile components in wind turbines. Therefore, the prediction of remaining useful life (RUL) of faulty or damaged wind turbine bearings will provide useful support for reliability evaluation and advanced maintenance of wind turbines. This paper proposes a data-driven method combining the interval whitenization method with a Gaussian process (GP) algorithm in order to predict the RUL of wind turbine generator bearings. Firstly, a wavelet packet transform is used to eliminate noise in the vibration signals and extract the characteristic fault signals. A comprehensive analysis of the real degradation process is used to determine the indicators of degradation. The interval whitenization method is proposed to reduce the interference of non-stationary operating conditions to improve the quality of health indicators. Finally, the GP method is utilized to construct the model which reflects the relationship between the RUL and health indicators. The method is assessed using actual vibration datasets from two wind turbines. The prediction results demonstrate that the proposed method can reduce the effect of non-stationary operating conditions. In addition, compared with the support vector regression (SVR) method and artificial neural network (ANN), the prediction accuracy of the proposed method has an improvement of more than 65.8%. The prediction results verify the effectiveness and superiority of the proposed method.