In this work the permeability of a model asymmetric plasma membrane, for ions, water and the anti-cancer drugs cisplatin and gemcitabine is studied by means of all-atom molecular dynamics simulations. It is shown for the first time that permeability of the highly curved membrane increases from one to three orders of magnitude upon membrane bending depending on the compound and the sign of curvature. Our results suggest that the membrane curvature could be an important factor of drug translocation through the membrane.