Since the health status of gas turbine engine is difficult to quantify, which brings great challenges to health assessment and remaining useful life predictions. To solve this problem, a gray target calculation and cloud gravity center (GTC–CGC) health assessment method is proposed. The three-dimensional data normalization process is to characterize the different initial states between samples. The empirical signal-to-noise ratio and entropy weight are used to calculate the subjective and objective weights of health indicators, and convex optimization is used to realize the fusion assessment. The sliding time window method is used to calculate the real-time health state of the gas turbine engine. Finally, health assessment and remaining useful life prediction tests were conducted on turbofan engines using the NASA C-MAPSS dataset. The experimental results show that compared with the self-organizing neural network, the monotonicity, robustness, and trend of the health assessment results were improved by 0.3216, 0.0843, and 0.0355, respectively. The third-order linear regression algorithm was used for remaining useful life prediction, the prediction score of this model is 265, and root mean squared error is 26.1542, which is equivalent to the prediction accuracy of mainstream intelligent prediction methods such as neural network.