An appropriate band structure and effective carrier separation are very important for the performance of a solar photocatalyst. In this paper, based on first-principles calculations, it was predicted that blue phosphorene (BlueP) and a C₂N monolayer can form a promising metal-free type-II heterojunction. The electronic structure of the BlueP/C₂N heterojunction facilitated the overall water splitting reactions well. The projected band structure showed that the conduction band edge was contributed by C₂N and the valence band edge was dominated by BlueP. Under the combination of the driving force of the band offset and the built-in electric field between the two layers, the photo-generated electrons and holes were transferred spontaneously to the conduction band of C₂N and the valence band of BlueP, respectively. An effective carrier separation in the heterostructure was thus achieved. More notably, the obtained light absorption of the BlueP/C₂N junction showed an obvious red-shift, which greatly extended the area of light adsorption to the visible light region. We further proposed that strain could also be used to modulate the band gap and the band edge positions of the heterojunction. Our results not only provide a theoretical design, but also reveal the fundamental separation mechanism of the photo-generated carriers in the BlueP/C₂N heterojunction.