Using first-principles calculations, we investigate the geometric structures, stabilities, electronic structures, and magnetic properties of three kinds of AsP monolayers: blue-phosphorene-like AsP (blue AsP), black-phosphorene-like AsP (black AsP) and puckered AsP. Stability analysis implies a high possibility of fabricating AsP monolayers in experiments. The blue AsP monolayer possesses the most stable structure with an indirect band-gap of 2.52 eV. The blue AsP system is also a good candidate for visible light photocatalytic decomposition of water. The black one is a semiconductor with a di...