The electronic and magnetic properties of (Cu, N) co-doped zinc oxide (ZnO) with different Cu:N ratios of 1:2, 1:1 and 2:1 have been studied based on the density functional theory. Mono-doping of Cu or N into ZnO keeps its direct band gap semiconductor nature and exhibits its [Formula: see text]-type conduction, half-metallic properties for valance band merging below the acceptor levels in a spin direction. However, co-doping of Cu and N into ZnO greatly enhances its conductivity of the system and makes it exhibit metallic properties, the metallic properties become more obvious as the ratio of Cu:N increases from 1:2 to 2:1. Furthermore, co-doping of Cu and N into ZnO can increase magnetic moment for the interaction among Cu [Formula: see text], N [Formula: see text] and O [Formula: see text]. ZnO:2Cu–N model is the most stable model in thermodynamics but it shows anti-ferromagnetism (FM) while ZnO:Cu–N system can achieve room-temperature FM, so Cu:N ratios of 1:1 may achieve better electronic and magnetic properties by comprehensive comparison.