Exploring two-dimensional valleytronic crystals with large valley-polarized state is of considerable importance due to the promising applications in next-generation information related devices.Here,we show first-principles evidence that single-layer NbX2 (X =S,Se) is potentially the long-sought two-dimensional valleytronic crystal.Specifically,the valley-polarized state is found to occur spontaneously in single-layer NbX2,without needing any external tuning,which arises from their intrinsic magnetic exchange interaction and inversion asymmetry.Moreover,the strong spin-orbit coupling strength within Nb-d orbitals renders their valley-polarized states being of remarkably large (NbS2 ~ 156 meV/NbSe2 ~ 219 meV),enalbling practical utilization of their valley physics accessible.In additional,it is predicted that the valley physics (i.e.,anomalous valley Hall effect) in single-layer NbX2 is switchable via applying moderate strain.These findings make single-layer NbX2 tantalizing candidates for realizing high-performance and controllable valleytronic devices.