We propose a new acceleration scheme by employing the enormous electric potential behind a light-pressure-driven piston, namely 'dragging field acceleration'. When a thin foil driven by light pressure of an ultra-intense laser pulse propagates in underdense background plasma, it serves as a shock-like piston, trapping and reflecting background protons to ultra-high energies. Unlike in shock wave acceleration, the piston velocity is not limited by the Mach number and can be highly relativistic. Background protons can be trapped and reflected forward by the 'dragging field' potential attached to a piston, which is not employed in light-pressure acceleration. Our one-dimensional particle-in-cell simulations and analytical model both show that proton energies of several tens to hundreds of GeV can be obtained. The injection conditions are investigated. Generation of mono-energetic tens-of-GeV proton bunch in twodimensional geometry are discussed. Finally, the scheme is demonstrated with a three-dimensional simulation, where the effect of radiation reaction is included.