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The process of electron ionization is studied in proton collision with atomic hydrogen in the five initial states (1s, 2s, 2p0, and 2p±1) at intermediate impact energies. The first- and second-Born approximations are applied to calculate the ionization differential cross sections. Double and single differential cross sections are calculated at low electron emission energies. The closured second-Born approximation is applied to calculate the double differential cross sections (DDCSs). At several ejected electron energies, the DDCS is obtained as a function of the projectile scattering angles and also as a function of the electron ejected angles. The single differential cross section (SDCS) is obtained as a function of the ejected electron energy using first-Born approximation. Comparisons are made with available experimental data and previous theoretical calculations.