We propose a novel excellent two-dimensional photocatalyst SnN3 monolayer using first-principles calculations. The stability of SnN3 monolayer have been examined via formation energy, phonon spectrum and ab initio molecular dynamics calculations. Large optical absorption capacity plays significant role in the enhancement of photocatalytic splitting of water. The SnN3 monolayer have ultra-high optical absorption capacity in visible region, which is as three and four times as that of SnP3 and MoS2 monolayer, respectively. Available potential and appropriate band positions indicating the ability of overall water splitting even in a wide strain range.Electronic properties of SnN3 monolayer can also be engineered effectively via the external strain, such as the conversion from in-direct band gap to direct band gap. The applied electric field splits the energy levels due to Stark effect, resulting in states accumulation and smaller gap width.