For the online early fault detection problem under non-stop scene, there are some challenges: 1) Monitoring signals are sequentially collected in unlabeled streaming form; 2) The normal operating process of bearings is easily interrupted by irregular noise, raising false alarms; 3) Most alarm thresholds are set with expert experience. With the merit that tensor decomposition can represent high-dimensional essential information of signal effectively, this paper proposes a new unsupervised tensor-based deep transfer learning approach. First, a tensor representation-based deep multi-task anomaly detection model is built. This model utilizes core tensor to construct the representation of one-class anomaly detection rule and establish hypersphere rule adaptation mechanism. Running with an alternative optimization of tensor decomposition and common feature extraction, this model can conduct effective transition of anomaly detection rule from offline bearings to online target bearing and realize anomaly detection of online unlabeled data. Second, a nonparametric alarm threshold setting method is designed based on sequential accumulation of anomalous probability. This method can adaptively determine online threshold only requiring the confidence level of false alarm. Moreover, a theoretical analysis about the threshold"s rationality is provided. Experimental results on the IEEE PHM Challenge 2012 dataset show that the proposed approach can obtain real-time detection performance and lower number of false alarm. The proposed approach is believed to supply a solution with better deployment and robustness.