Wind turbine (WT) condition monitoring and anomaly detection based on Supervisory Control and Data Acquisition (SCADA) data are helpful for wind power operators to organize operation and maintenance schedules for WTs. However, because of the volatility of wind, most of the measurements related to WTs are time-varying and operating condition dependent. Therefore, how to detect the anomaly from measurements as soon as possible under different operating conditions becomes one of the most crucial issues to ensure the normal operation of WTs. In this paper, an anomaly detection method for gearbox oil temperature using SCADA data is proposed based on the Sparse Bayesian Learning (SBL) and hypothesis testing (HT). For each operating condition, the possible variation range of the oil temperature at a given confidence level is estimated according to historical data by using SBL. Then, the anomaly can be detected by observing whether the actual value of the temperature falls into the estimated interval at an enough high possibility, which can be checked by using HT. The proposed method combines the probability estimation with HT, which can perform reliable and timely anomaly detection due to it can eliminate the influence of operating conditions and other factors on the gearbox oil temperature. The effectiveness of the proposed method is tested on two WTs with known gearbox oil temperature over-limit faults. Testing results and experimental comparison with the similar gearbox oil temperature anomaly detection methods demonstrate the superiority of the proposed method.