Similar to pure graphyne, two-dimension carbon nitride graphyne also possesses exceptional properties and potential applications. In this work, by using the density functional theory (DFT) and combining with nonequilibrium Green's function (NEGF), we study the electronic band structures and transport properties of zigzag rhombic N-graphyne nanoribbons (ZrNGYNRs). Our results show that all of the ZrNGYNRs have similar metallic band structures in no magnetic and ferromagnetic configuration, while the transport properties are directly related to the symmetry of the systems. The electron band stru...