Unrestricted emission of volatile organic compounds (VOCs)─a threat to human health and the environment─can be controlled to a large extent by the capturing mechanism. Few recent experimental studies explored the efficacy of the deep eutectic solvent (DES), a designer solvent with some fascinating properties, as a VOC-capturing medium. Through the partition coefficient measurement, it was found that the choline chloride-based DESs exhibit excellent VOC-capturing potencies. However, a molecular picture of the above absorption process is still lacking. Here, we study the molecular mechanism of the absorption of two commonly occurring VOCs, toluene and acetaldehyde, in two different choline chloride-based DESs with varying donor molecules, urea, and levulinic acid via the molecular dynamics simulation technique. Strong absorption of the VOCs is observed in both the DESs. The free energy profile for the absorption process has been explored using the umbrella sampling method. The VOCs are preferentially solvated near the liquid/vapor interface. The simulated partition coefficients for the VOCs from the vapor to the liquid phase show good agreement with the experimental results. Detailed analyses of the spatial and orientational structure of the VOCs and different components of DESs are performed to elucidate the interaction among them. The above analyses have indicated that DES is a better VOC-capturing medium compared to a room-temperature ionic liquid, which is more extensively studied in the literature.