This study is focused on the punching strength of fiber-reinforced polymer (FRP) concrete slabs. The mechanical properties of reinforced concrete slabs are often constrained by their punching shear strength at the column connection regions. Researchers have explored the use of fiber-reinforced polymer reinforcement as an alternative to traditional steel reinforcement to address this limitation. However, current codes poorly calculate the punching shear strength of FRP-reinforced concrete slabs. The aim of this study was to create a robust model that can accurately predict its punching shear strength, thus improving the analysis and design of composite structures with FRP-reinforced concrete slabs. In this study, 189 sets of experimental data were collected, and six machine learning models, including linear regression, support vector machine, BP neural network, decision tree, random forest, and eXtreme Gradient Boosting, were constructed and evaluated based on goodness of fit, standard deviation, and root-mean-square error in order to select the most suitable model for this study. The optimal model obtained was compared with the models proposed by codes and the researchers. Finally, a model explainability study was conducted using SHapley Additive exPlanations (SHAP). The results showed that random forests performed best among all machine learning models and outperformed existing models suggested by codes and researchers. The effective depth of the FRP-reinforced concrete slabs was the most important and proportional to the punching shear strength. This study not only provides guidance on the design of FRP-reinforced concrete slabs but also informs future engineering practice.