In this work, we performed a density functional theory calculation to systematically investigate the adsorption and evaluate the adsorption performance of aromatic volatile organic compounds, benzene and toluene, on WSe2 monolayer. The most favourable adsorption configurations of gas molecules with the parallel orientation of the benzene ring to the substrate surface are explored by computing the binding energies as a function of spatial coordinates and carefully optimizing geometrical structures. The calculations pointed out that gas molecules could diffuse across the substrate along the diffusion paths with quite low diffusion potential barriers, about 180 meV for benzene and 130 meV for toluene molecules. We found that both gases are physisorbed on WSe2 monolayer with moderate adsorption energies, short recovery times, and large response lengths. The gas adsorption causes the bandgap reduction of 26 meV and a slight work function increase of the substrate. There is a charge transfer from the substrate onto the gas molecules, this may cause a resistance decrease of the p-type semiconductor substrate. WSe2 monolayer is quite sensitive to benzene and toluene, and could be suggested as an aromatic gas sensing material.