The structural, elastic, magnetic, and electronic properties of the tetragonal zircon-type CeVO 4 are investigated with first-principles method. We use the local density approximation (LDA), generalized gradient approximation (GGA), LDA+U, and GGA+U methods to find the most stable structure of the zircon-type CeVO 4 . By employing pure density functional theory (DFT), we obtain a ferromagnetic (FM) metallic ground state, which is in disagreement with experiments; While LDA+U (U=6eV) can give an antiferromagnetic (AFM) insulating ground state for CeVO 4 , according well with the experimental finding. For the AFM CeVO 4 , LDA+U calculation gives a band gap of 2.957eV and a magnetic moment of 1.03μ B per Ce atom, which are in good accordance with the experimental results. In addition, the elasticity-related properties, such as the elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio and Debye temperature, are also systematically investigated. The calculated bulk modulus of CeVO 4 is 100.6GPa, which agrees with the experimental result of 112GPa. The partial density of states (PDOS) and Mulliken populations are also analyzed.