Particle acceleration using ultraintense, ultrashort laser pulses is one of the most attractive topics in relativistic laser-plasma research. We report proton and/or ion acceleration in the intensity range of 5×10^{19} to 3.3×10^{20} W/cm^{2} by irradiating linearly polarized, 30-fs laser pulses on 10-to 100-nm-thick polymer targets. The proton energy scaling with respect to the intensity and target thickness is examined, and a maximum proton energy of 45 MeV is obtained when a 10-nm-thick target is irradiated by a laser intensity of 3.3×10^{20} W/cm^{2}. The proton acceleration is explained by a hybrid acceleration mechanism including target normal sheath acceleration, radiation pressure acceleration, and Coulomb explosion assisted-free expansion. The transition of proton energy scaling from I^{1/2} to I is observed as a consequence of the hybrid acceleration mechanism. The experimental results are supported by two- and three-dimensional particle-in-cell simulations.