In spite of the development of the Prognostics and Health Management (PHM) during past decades, the reliability prognostics of engineered systems under time-varying external conditions still remains a challenge in such a field. When considering the challenge mentioned above, a hybrid method for predicting the reliability index and the Remaining Useful Life (RUL) of engineered systems under time-varying external conditions is proposed in this paper. The proposed method is competent in reflecting the influence of time-varying external conditions on the degradation behaviour of engineered systems. Based on a subset of the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset as case studies, the Cox Proportional Hazards Model (Cox PHM) with time-varying covariates is utilised to generate the reliability indices of individual turbofan units. Afterwards, a Vector Autoregressive model with Exogenous variables (VARX) combined with pairwise Conditional Granger Causality (CGC) tests for sensor selections is defined to model the time-varying influence of sensor signals on the reliability indices of different units that have been previously generated by the Cox PHM with time-varying covariates. During the reliability prediction, the Fourier Grey Model (FGM) is employed with the time series models for long-term forecasting of the external conditions. The results show that the method that is proposed in this paper is competent for the RUL prediction as compared with baseline approaches.