The prediction of total pressure at the outlet of an engine's high-pressure compressor is a critical issue within the Full Authority Digital Engine Control (FADEC) system. This paper presents a time series-based model for the prediction of total pressure and introduces a Gradient Boosting Random Forest (GBRF) algorithm, which leverages the synergistic benefits of Random Forest (RF) and Gradient Boosting Decision Tree (GBDT) methodologies. A comprehensive comparative analysis with traditional RF and GBDT algorithms was conducted through extensive simulation experiments to validate and evaluate the proposed GBRF algorithm. Following this, a holistic framework for training, learning, and prediction was established. The results demonstrate the efficacy of the GBRF algorithm in preventing overfitting and its capacity to elevate the accuracy of the test set in proportion to the enhanced accuracy of the training set.