The ECPSSR theory to calculate the inner-shell ionization cross sections by light-ion impact is studied. Starting from the general formulation of the plane-wave Born approximation, the corrections for the energy-loss effect (E) and the Coulomb-deflection effect (C) of the projectile, and for the binding-polarization effect in the perturbed-stationary-state approach (PSS) and the electronic relativistic effect (R) of the target electron are described. The calculated values in the ECPSSR theory are compared with the experimental data. In general, agreement is good, but there are systematic deviations for low-energy projectiles. The comparison with other theoretical treatments for the inner-shell ionization is discussed.