Gas-sensing properties of nitrogenated holey graphene (C2N), graphdiyne (GDY) and their van der Waals heterostructure (C2N…GDY) have been studied towards particular volatile organic compounds (VOCs) by means of spin-polarized, dispersion-corrected DFT calculations. We find that VOCs such as acetone, ethanol, propanal, and toluene interact weakly with the GDY monolayer; however, the bindings are significantly enhanced with the C2N monolayer and the hybrid C2N…GDY heterostructure in AB stacking. Electron localization function (ELF) analysis shows that all VOCs are van der Waals bound (physical binding) to the 2D materials, which result in significant changes of the charge density of C2N and GDY monolayers and the C2N…GDY heterostructure. These changes alter the electronic properties of C2N and GDY, and the C2N…GDY heterostructure, upon VOC adsorption, which are investigated by density-of-states plots. We further apply thermodynamic analysis to study the sensing characteristics of VOCs under varied conditions of pressure and temperature. Our findings clearly indicate that the C2N…GDY heterostructure is a promising material for sensing of certain VOCs.