Particle acceleration using ultraintense, ultrashort laser pulses is one of the most attractive topics in relativistic laser-plasma research. We report proton/ion acceleration in the intensity range of 5×10 19 W/cm 2 to 3.3×10 20 W/cm 2 by irradiating linearly polarized, 30-fs, 1-PW laser pulses on 10-to 100-nm-thick polymer targets. The proton energy scaling with respect to the intensity and target thickness was examined. The experiments demonstrated, for the first time with linearly polarized light, a transition from the target normal sheath acceleration to radiation pressure acceleration and showed a maximum proton energy of 45 MeV when a 10-nm-thick target was irradiated by a laser intensity of 3.3×10 20 W/cm 2. The experimental results were further supported by two-and three-dimensional particle-in-cell simulations. Based on the deduced proton energy scaling, proton beams having an energy of ~ 200 MeV should be feasible at a laser intensity of 1.5×10 21 W/cm 2 .