Using one of the world most powerful laser facility, we demonstrate for the first time that high-contrast multi-picosecond pulses are advantageous for proton acceleration. By extending the pulse duration from 1.5 to 6 ps with fixed laser intensity of 1018 W cm-2, the maximum proton energy is improved more than twice (from 13 to 33 MeV). At the same time, laser-energy conversion efficiency into the MeV protons is enhanced with an order of magnitude, achieving 5% for protons above 6 MeV with the 6 ps pulse duration. The proton energies observed are discussed using a plasma expansion model newly developed that takes the electron temperature evolution beyond the ponderomotive energy in the over picoseconds interaction into account. The present results are quite encouraging for realizing ion-driven fast ignition and novel ion beamlines.