We study the high-energy (1-4 MeV) proton production from a slab plasma irradiated by a ultrashort high-power laser. In our 2.5-dimensional particle-in-cell simulations, a p-polarized laser beam of 1.6 x 10(19) W/cm(2), 300 fs, lambda(L)=1.053 microm, illuminates a slab plasma normally; the slab plasma consists of a hydrogen plasma, and the target plasma thickness and the laser spot size are 2.5lambda(L) and 5lambda(L), respectively. The simulation results show that an emitted proton energy depends on the slab plasma density, and three kinds of high-energy proton beams are generated at the target plasma surfaces: one kind of the proton beams is produced at the laser-illuminated target surface and accelerated to the same laser-incident side. The second is generated at the target surface opposite to the laser-illuminated target surface and is accelerated outward on the same side. The third is generated at the laser-illuminated target surface and accelerated to the opposite side while passing through the target plasma. The simulations also show a mechanism of proton accelerations. In an overdense plasma, laser energy goes to energies of hot electrons and magnetic fields in part; the electrons oscillate around the slab plasma so that a static electric field is generated and consequently protons are extracted. The magnetic field generated in the slab plasma exists longer and heats up the plasma electrons to sustain the static electric field even after the laser termination.