Recently, deep learning technology-based neural networks have been adopted for remaining useful life (RUL) prediction of rotating machines. However, there are still some shortcomings: (1) an individual degradation feature cannot sufficiently represent the degradation process, which has an adverse impact on the accuracy of prediction results; (2) most recurrent neural network-based prediction methods have difficulty in quantifying the uncertainty of the forecast results. In this paper, a fusing sensitive degradation features with uncertainty analysis for RUL prediction of rotating machines is proposed. Firstly, the statistical features contained in the vibration signal used to monitor the degradation of rotating equipment are extracted to construct the original feature set. Then, the weight coefficients of the monotonicity, correlation and robustness criteria are determined by the self-adjusting analytic hierarchy process. The sensitive features that describe the degradation process are selected from among the statistical features. Furthermore, the sensitive features are fed into residual networks and gated recurrent unit, and the spatial and temporal correlation of the features are considered to establish the health index (HI). Finally, the fitted HI is input into a Gaussian process regression model, and the prediction results with confidence intervals are obtained. To verify the effectiveness and superiority of the proposed method, two public bearing datasets and three model methods are used for comparative experiments.