Remaining useful life (RUL) prediction can provide additional capabilities to condition-based maintenance (CBM) and predictive maintenance (PdM) for the reliability and service life of a system. Time-varying operational conditions, such as the altitude, Mach number, and throttle resolver angle of an aero-engine, could result in two main challenges for RUL predictions: varying degradation rates and abrupt jumps in the amplitude of sensor readings. Our study addresses these two challenges in the data pre-processing stage, through operational condition features and the multi-operational condition-based normalization method (MOC-based Normalization). In the framework of our model, first, two density-based clustering algorithms are integrated to be a new classifier for operational conditions clustering and identification in an unsupervised manner. Then, operational condition features consisting of operational condition labels and an operational condition factor are conducted. In the meantime, the proposed MOC-based Normalization recalibrates the upward or downward abrupt jumps of sensor readings at the operational conditions change-points. Sensor data features and operational condition features are combined in the last step of the data pre-processing stage. On this basis, the RUL representation model is trained with the combined features through a gated recurrent unit (GRU)-based network with only two layers in the hidden layer. Experiments on benchmark datasets have been conducted. The results show that the MOC-based Normalization efficiently mitigates the jumps on sensor readings, and the operational condition features improve the prognostic model. Approximately 10% RMSE improvements over the top-three state-of-the-art algorithms are achieved in the RUL prediction under time-varying operational conditions.