Deep learning is widely used in remaining useful life (RUL) prediction because it does not require prior knowledge and has strong nonlinear fitting ability. However, most of the existing prediction methods are point prediction. In practical engineering applications, confidence interval of RUL prediction is more important for maintenance strategies. This paper proposes an interval prediction model based on Long ShortTerm Memory (LSTM) and lower upper bound estimation (LUBE) for RUL prediction. First, convolutional auto-encode network is used to encode the multi-dimensional sensor data into one-dimensional features, which can well represent the main degradation trend. Then, the features are input into the prediction framework composed of LSTM and LUBE for RUL interval prediction, which effectively solves the defect that the traditional LUBE network cannot analyze the internal time dependence of time series. In the experiment section, a case study is conducted using the turbofan engine data set CMAPSS, and the advantage is validated by carrying out a comparison with other methods.