Focusing processes of rotating and propagating proton beams in a neutral hydrogen gas are studied numerically by using a two-dimensional hybrid code. Processes including beam impact ionization, plasma avalanche and field emission are taken into consideration. The plasma formation time depends on the initial gas density and the beam intensity. When 2-Torr neutral gas is filled initially, enough plasma density is created by the rising part of the beam pulse, so that the main pulse is focused and forms a rotating and propagatingbeam configuration.