The adsorption mechanism of individual volatile organic compounds (VOCs) on the surface of graphene is investigated using nonempirical van der Waals (vdW) density functional theory. The VOCs chosen as adsorbates are ethanol, benzene, and toluene, which are found in the exhaled breath of lung cancer patients. The most energetically favorable configurations of the adsorbed systems, adsorption energy profiles, charge transfer, and work function are calculated. The fundamental insight into the interactions between the considered VOC molecules and graphene through molecular doping, i.e., charge transfer, is estimated. It is found that the adsorption energy is highly sensitive to the vdW functionals. Adsorption energies calculated by revPBE-vdW are in good agreement with the available experimental data, and the revPBE-vdW functional can cover well the physical phenomena behind the adsorption of these VOCs on graphene. Bader charge analysis shows that 0.064, 0.042, and 0.061e of charge were transferred from the graphene surface to ethanol, benzene, and toluene, respectively. All of the considered VOCs act as electron acceptors from graphene. By analyzing the electronic structure of the adsorption systems, we found that the energy level of the highest occupied molecular orbitals of these considered VOCs is shifted backward toward the Fermi level. The interaction of the VOCs with the π and π* states of the C atoms in graphene breaks the symmetry of graphene, leading to the opening of a band gap at the Fermi level. The adsorption of these considered VOCs onto the pristine graphene produces a band gap of 5-12 meV.