In the present work we describe a new approach, which uses topology of crystals for physicochemical properties prediction using artificial neural networks (ANN). The topologies of 268 crystal structures were determined using ToposPro software. Quotient graphs were used to identify topological centers and their neighbors. The topological approach was illustrated by training ANN to predict molar heat capacity, standard molar entropy and lattice energy of 268 crystals with different compositions and structures (metals, inorganic salts, oxides, etc.). ANN was trained using Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Mean absolute percentage error of predicted properties was ≤8 %.