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The rapid spread of COVID-19 has resulted in a large number of infections and significant economic impact on countries worldwide, and COVID-19 testing is one of the important methods to identify infected individuals. The previous studies have indicated that with improved COVID-19 testing capabilities, more confirmed cases can be detected. Therefore, how to accurately forecast the COVID-19 testing capabilities is a key issue in controlling the spread of the pandemic. In this study, based on a dataset of COVID-19 including data from 184 countries and 893 regions, we propose a novel machine learning framework named BO–SHAP–BLS, which combines Shapley Additive Explanations (SHAP), Bayesian Optimization (BO), and Broad Learning System (BLS), for forecasting COVID-19 testing capabilities. Firstly, SHAP is used to analyze and rank the importance of the original features. Then, BO is adopted to optimize both the hyperparameters of BLS and the number of features simultaneously. Finally, BLS is adopted to predict the number of COVID-19 tests in various countries. Experimental results show that BO–SHAP–BLS significantly outperforms the other machine learning models, indicating higher accuracy in predicting the COVID-19 testing capabilities. [ABSTRACT FROM AUTHOR]