In the realm of prognosticating the remaining useful life (RUL) of pivotal components, such as aircraft engines, a prevalent challenge persists where the available historical life data often proves insufficient. This insufficiency engenders obstacles such as impediments in performance degradation feature extraction, inadequacies in capturing temporal relationships comprehensively, and diminished predictive accuracy. To address this issue, a 1D CNN-GRU prediction model for few-shot conditions is proposed in this paper. In pursuit of more comprehensive data feature extraction and enhanced RUL prognostication precision, the Convolutional Neural Network (CNN) is selected for its capacity to discern high-dimensional features amid the intricate dynamics of the data. Concurrently, the Gated Recurrent Unit (GRU) network is leveraged for its robust capability in extracting temporal features inherent within the data. We combine the two to construct a CNN-GRU hybrid network. Moreover, the integration of data distribution alongside correlation and monotonicity indices is employed to winnow the input of multi-sensor monitoring parameters into the CNN-GRU network. Finally, the engine RULs are predicted by the trained model. In this paper, experiments are conducted on a sub-dataset of the National Aeronautics and Space Administration (NASA) C-MAPSS multi-constraint dataset to validate the effectiveness of the method. Experimental results have demonstrated that this method has high accuracy in RUL prediction tasks, which can powerfully demonstrate its effectiveness.