We present a new approach to estimate the binding affinity from given three-dimensional poses of protein-ligand complexes. In this scheme, every protein-ligand atom pair makes an additive free-energy contribution. The sum of these pairwise contributions then gives the total binding free energy or the logarithm of the dissociation constant. The pairwise contribution is calculated by a function implemented via a neural network that takes the properties of the two atoms and their distance as input. The pairwise function is trained using a portion of the PDBbind 2018 data set. The model achieves good accuracy for affinity predictions when evaluated with PDBbind 2018 and with the CASF-2016 benchmark, comparing favorably to many scoring functions such as that of AutoDock Vina. The framework here may be extended to incorporate other factors to further improve its accuracy and power.