This paper presents a data-driven framework that can accurately predict the buckling loads of composite near-spherical shells (i.e., variants of regular icosahedral shells) under external pressure. This framework utilizes finite element simulations to generate data to train a machine learning regression model based on the open-source algorithm Extreme Gradient Boosting (XGBoost). The trained XGBoost machine learning model can then predict buckling loads of near-spherical shells with a small margin of error without time-consuming finite element simulations. Examples of near-spherical composite shells with various geometries and material layups demonstrate the efficiency and accuracy of the framework. The machine learning model removes the demanding hardware and software requirements on computing buckling loads of near-spherical shells, making it particularly suitable to users without access to those computational resources.