The number of states required for describing a many-body quantum system increases exponentially with the number of particles; thus, it is time- and effort-consuming to exactly calculate molecular properties. Herein, we propose a deep learning algorithm named block-based graph neural network (BGNN) as an approximate solution. The algorithm can be understood as a representation learning process to extract useful interactions between a target atom and its neighboring atomic groups. Compared to other graph model variants, BGNN achieved the smallest mean absolute errors in most tasks on two large molecular datasets, QM9 and Alchemy. Our advanced machine learning method exhibits general applicability and can be readily employed for bioactivity prediction and other tasks relevant to drug discovery and materials design.