Structure–function relationships in proteins have been one of the crucial scientific topics. Heme proteins have diverse and pivotal biological functions. Therefore, clarifying their structure–function correlation is significant to understand their functional mechanism and is informative for various fields of science. In this study, we constructed convolutional neural network models for predicting protein functions from the tertiary structures of heme-binding sites (active sites) of heme proteins to examine the structure–function correlation. As a result, we succeeded in the classification of oxygen-binding protein (OB), oxidoreductase (OR), proteins with both functions (OB–OR), and electron transport protein (ET) with high accuracy. Although the misclassification rate for OR and ET was high, the rates between OB and ET and between OB and OR were almost zero, indicating that the prediction model works well between protein groups with very different functions. However, predicting the function of proteins modified with amino acid mutation(s) remains a challenge. Our findings indicate a structure–function correlation in the active site of heme proteins. This study is expected to be applied to the prediction of more detailed protein functions such as catalytic reactions.