This study proposes a machine learning-based approach for detecting sensor faults in wind turbines. The approach combines the Gaussian process regression (GPR) model and the Exponentially Weighted Moving Average (EWMA) monitoring chart, which provides sensitivity in detecting small shifts in the process mean. The detection threshold is computed using Kernel Density Estimation, which adds flexibility to the EWMA chart. We adopted Bayesian optimization to optimize the hyperparameters of the GPR model based on anomaly-free data. The proposed approach is tested on different sensor faults and compared with support Vector regression-based methods. The results show that the proposed approach effectively detects various types of sensor faults, including sensor faults in pitch angle measurement and generator speed measurement, and outperforms the support Vector regression-based approach.