Using first-principles theory, this work investigated the Cu-doping behavior on the N-vacancy of the C3N monolayer and simulated the adsorption performance of Cu-doped C3N (Cu–C3N) monolayer upon two dissolved gases (H2 and C2H2). The calculations meant to explore novel candidate for sensing application in the field of electrical engineering evaluating the operation status of the transformers. Our results indicated that the Cu dopant could be stably anchored on the N- vacancy with the Eb of − 3.65 eV and caused a magnetic moment of 1 μB. The Cu–C3N monolayer has stronger performance upon C2H2 adsorption than H2 give the larger Ead, QT and change in electronic behavior. The frontier molecular orbital (FMO) theory indicates that Cu–C3N monolayer has the potential to be applied as a resistance-type sensor for detection of such two gases, while the work function analysis evidences its potential as a field-effect transistor sensor as well. Our work can bring beneficial information for exploration of novel sensing material to be applied in the field of electrical engineering, and provide guidance to explore novel nano-sensors in many fields.