Herein, we proposed a novel excellent two-dimensional photocatalyst, the SnN3 monolayer, using first-principles calculations. The stability of the SnN3 monolayer was examined via formation energy, phonon spectroscopy and ab initio molecular dynamics simulations. The SnN3 monolayer has an ultra-high optical absorption capacity of the order of 105 cm-1 in the visible region, which is 3, 4 and 10 times those of SnP3, MoS2 and g-C3N4 monolayers, respectively. Moreover, it has a higher carrier mobility, 769.19 cm2 V-1 s-1, than the other monolayers; the available electrostatic potential of -5.02 eV and the appropriate band gap of 1.965 eV indicate its applicability as a catalyst for overall water splitting over a wide strain range. The electronic properties of the SnN3 monolayer could also be engineered effectively by altering the external strain and electric field.