Nitrate reduction to ammonia has attracted much attention for nitrate (NO) removal and ammonia (NH) production. Identifying promising catalyst for active nitrate electroreduction reaction (NORR) is critical to realize efficient upscaling synthesis of NH under low-temperature condition. For this purpose, by means of spin-polarized first-principles calculations, the NORR performance on a series of graphitic carbon nitride (g-CN) supported double-atom catalysts (denoted as MM@g-CN) are systematically investigated. The synergistic effect of heterogeneous dual-metal sites can bring out tunable activity and selectivity for NORR. Amongst 21 candidates examined, FeMo@g-CN and CrMo@g-CN possess a high performance with low limiting potentials of -0.34 and -0.39 V, respectively. The activities can be attributed to a synergistic effect of the MM dimer d orbitals coupling with the anti-bonding orbital of NO. The dissociation of deposited FeMo and CrMo dimers into two separated monomers is proved to be difficult, ensuring the kinetic stability of MM@g-CN. Furthermore, the dual-metal decorated on g-CN significantly reduces the bandgap of g-CN and broadens the adsorption window of visible light, implying its great promise for photocatalysis. This work opens a new avenue for future theoretical and experimental design related to NORR photo-/electrocatalysts.