We have developed a theoretical and computational model to study the initiation phase of pseudospark discharges in a hollow cathode via a quasi-three-dimensional electrostatic particle-in-cell plus Monte Carlo collision(PIC/MCC) method. The numerical results clearly identified different processes of ionization growth. It has been found that the ionization processes are determined by hollow cathode effect and local electric field. The growth is dependent on α ionization multiplication due to local space charge in the stage from initial ionization growth to the onset of the hollow cathode effect, and then the hollow cathode effect becomes the leading factor.