In view of easily interfered properties of bearing incipient fault signal, it is beneficial to mine more useful information from vibration signal for bearing state monitoring. For exploring local information and utilizing correlation between the characteristic of different frequency bands, feature tensor based on Wavelet Packet (WP) decomposition is introduced to characterize bearing fault state as reflected by vibration signal. Then the bearing state monitoring can be transformed as a one-class classification problem in tensor space, in which the abnormal samples represent the fault states and the normal samples mean the health states of the bearings, respectively. Combining with Support Tensor Data Description (STDD), an early fault detection method is proposed by employing feature tensor correlating with bearing fault directly. To further quantify the fault degree of bearing, a tensor-based anomaly index (AIt) is presented by taking advantage of the distance between feature tensor sample to spherical surface generated by STDD in tensor space. Experimental results of bearing verify that the proposed tensor-based fault detection method is effective for bearing early fault detection, and AIt is sensitive to bearing operation state and therefore suitable for fault degradation tracking. Further experiments show that the tensor-based method is robust to noise and small sample size problem.