Considering the safety and economic factors, most of the performance degradation data of historical equipment are truncated type. The challenge of zero life label is encountered when deep learning training is adopted, quantifying the uncertainty of remaining useful life (RUL) is even more difficult, and what is more, the existing deep learning models ignore the difference between the first hitting and non-first hitting time meanings when predicting the RUL. To overcome the above difficulties, this paper proposes a method over RUL prediction for degraded equipment under zero life label. Data preprocessing technology is utilized to generate samples labeled with degradation information, and the evolution law of equipment performance degradation is described by Bayesian bidirectional long short-term memory (B-Bi-LSTM) model. At the same time, the uncertainty measurement of performance degradation is realized by means of variational inference technology. Furthermore, the relationship between the performance degradation prediction distribution and the RUL distribution is analyzed from the perspective of reliability, and the RUL probability distribution of the equipment is derived from the point of the first hitting and non-first hitting time respectively. The proposed method is verified by a case of lithium battery. The experimental results show that the proposed method can provide the point estimation and probability distribution results of RUL prediction, which can effectively ensure the scientificity of the prediction results.