The development of catalysts for the electrochemical N2 reduction reaction (NRR) with a low limiting potential and high Faradaic efficiency is highly desirable but remains challenging. Here, to achieve acceleration, we develop and report a slab graph convolutional neural network (SGCNN), an accurate and flexible machine learning (ML) model that is suited for probing surface reactions in catalysis. With a self-accumulated database of 3040 surface calculations at the density-functional-theory (DFT) level, SGCNN predicted the binding energies, ranging over 8 eV, of five key adsorbates (H, N2, N2H, NH, NH2) related to NRR performance with a mean absolute error (MAE) of only 0.23 eV. SGCNN only requires the low-level inputs of elemental properties available in the periodic table of elements and connectivity information of constituent atoms; thus, accelerations can be realized. Via a combined process of SGCNN-driven predictions and DFT verifications, four novel catalysts in the L12 crystal space, including V3Ir(111), Tc3Hf(111), V3Ni(111), and Tc3Ta(111), are proposed as stable candidates that likely exhibit both a lower limiting potential and higher Faradaic efficiency in the NRR, relative to the reference Mo(110). The ML work combined with a statistical data analysis reveals that catalytic surfaces with an average d-orbital occupation between 4 and 6 could lower the limiting potential and potentially overcome the scaling relation in the NRR.