Recently, graphyne-based gas sensors have drawn a lot of interest. One kind of graphene with acetylene bonds connecting its hexagons is graphyne. In this study, the density functional theory (DFT) method was used to investigate the physical parameters of the surface adsorption of carbon monoxide on the [Formula: see text]- and [Formula: see text]-graphyne nanosheet, taking into account van der Waals (vdW) interactions through the use of the SIESTA computational code. CO molecule adsorbed and optimized in two vertical and horizontal states from the side of carbon and oxygen atoms, at different distances and sites relative to the graphyne sheet. After optimization and finding the adsorption energy, the best adsorption sites, equilibrium distance of the molecule from the surface, electronic structure, charge transfer rate, and bandgap changes were calculated. It was observed that the changes in the electronic structure after the adsorption of CO molecule are insignificant and the [Formula: see text]- and [Formula: see text]-graphyne nanosheets remained zero-gap and narrow-gap semiconductors, respectively. The adsorption of CO molecule on the [Formula: see text]- and [Formula: see text]-graphyne nanosheets is physisorption. The results show that the [Formula: see text]-graphyne nanosheet has a good potential for adsorbing and detecting CO molecules and sensor applications.