Three two-dimensional phosphorus nitride (PN) monolayer sheets (named as α-, β-, and γ-PN, respectively) with fantastic structures and properties are predicted based on first-principles calculations. The α-PN and γ-PN have a buckled structure, whereas β-PN shows puckered characteristics. Their unique structures endow these atomic PN sheets with high dynamic stabilities and anisotropic mechanical properties. They are all indirect semiconductors and their band gap sensitively depends on the in-plane strain. Moreover, the nanoribbons patterned from these three PN monolayers demonstrate a remarkable quantum size effect. In particular, the zigzag α-PN nanoribbon shows size-dependent ferromagnetism. Their significant properties show potential in nano-electronics. The synthesis of the three phases of the PN monolayer sheet is proposed theoretically, which is deserving of further study in experiments.