We predict the adsorption proficiency of hexagonal boron nitride (h-BN) sheets to toxic gas molecules like CO2, H2S and NO2 on the basis of first-principles density functional theory calculations. The computed energies predict the pristine h-BN sheet to have very little affinity towards the mentioned gas molecules. However, while doping C at the N site of the h-BN sheet brings a significant enhancement to the estimated adsorption energies, doping C at B site of the sheet is found to be energetically not so favorable. To have a higher coverage effect, the concentration of C doping on the h-BN sheet is further increased which resulted in upsurging the adsorption energies for the mentioned gas molecules. Among the three, CO2, H2S are found to be physisorbed to the C-doped h-BN sheets, where as the C-doped sheets are found to have strong affinity towards NO2 gas molecules.