Basalt fiber-reinforced concrete (BFRC) represents a form of high-performance concrete. In structural design, a 28-day resting period is required to achieve compressive strength. This study extended an extreme gradient boosting tree (XGBoost) hybrid model by incorporating genetic algorithm (GA) optimization, named GA-XGBoost, for the projection of compressive strength (CS) on BFRC. GA optimization may reduce many debugging efforts and provide optimal parameter combinations for machine learning (ML) algorithms. The XGBoost is a powerful integrated learning algorithm with efficient, accurate, and scalable features. First, we created and provided a common dataset using test data on BFRC strength from the literature. We segmented and scaled this dataset to enhance the robustness of the ML model. Second, to better predict and evaluate the CS of BFRC, we simultaneously used five other regression models: XGBoost, random forest (RF), gradient-boosted decision tree (GBDT) regressor, AdaBoost, and support vector regression (SVR). The analysis results of test sets indicated that the correlation coefficient and mean absolute error were 0.9483 and 2.0564, respectively, when using the GA-XGBoost model. The GA-XGBoost model demonstrated superior performance, while the AdaBoost model exhibited the poorest performance. In addition, we verified the accuracy and feasibility of the GA-XGBoost model through SHAP analysis. The findings indicated that the water–binder ratio (W/B), fine aggregate (FA), and water–cement ratio (W/C) in BFRC were the variables that had the greatest effect on CS, while silica fume (SF) had the least effect on CS. The results demonstrated that GA-XGBoost exhibits exceptional accuracy in predicting the CS of BFRC, which offers a valuable reference for the engineering domain.