Effective condition monitoring and fault diagnosis of wind turbines are crucial for avoiding serious damages to wind turbines. The supervisory control and data acquisition (SCADA) system of a wind turbine provides valuable insights into turbine performance. In order to make full use of such valuable information, this paper investigates fault diagnosis of wind turbines by using Gaussian process classifiers (GPC) to the operational data collected from the SCADA system. Both real-time and predictive fault diagnosis were considered. As an alternative to the support vector machine (SVM) technique, the GPC possesses the capability of providing probabilistic information about the fault types, which is valuable for making maintenance plan in real practice. The comparison results show that the GPC method is able to provide more accurate fault diagnosis results than the SVM technique on average.