Predictive maintenance based on performance degradation is a crucial way to reduce maintenance costs and potential failures in modern complex engineering systems. Reliable remaining useful life (RUL) prediction is the main criterion for decision-making in predictive maintenance. Conventional model-based methods and data-driven approaches often fail to achieve an accurate prediction result using a single model for a complex system featuring multiple components and operational conditions, as the degradation pattern is usually nonlinear and time-varying. This paper proposes a novel multi-scale RUL prediction approach adopting the Long Short-Term Memory (LSTM) neural network. In the feature engineering phase, Pearson’s correlation coefficient is applied to extract the representative features, and an operation-based data normalisation approach is presented to deal with the cases where multiple degradation patterns are concealed in the sensor data. Then, a three-stage RUL target function is proposed, which segments the degradation process of the system into the non-degradation stage, the transition stage, and the linear degradation stage. The classification of these three stages is regarded as the small-scale RUL prediction, and it is achieved through processing sensor signals after the feature engineering using a novel LSTM-based binary classification algorithm combined with a correlation method. After that, a specific LSTM-based predictive model is built for the last two stages to produce a large-scale RUL prediction. The proposed approach is validated by comparing it with several state-of-the-art techniques based on the widely used C-MAPSS dataset. A significant improvement is achieved in RUL prediction performance in most subsets. For instance, a 40% reduction is achieved in Root Mean Square Error over the best existing method in subset FD001. Another contribution of the multi-scale RUL prediction approach is that it offers more degree of flexibility of prediction in the maintenance strategy depending on data availability and which degradation stage the system is in.