The electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane in an a:b electrolyte solution, taking the effect of the sizes of charged species into account, is analyzed theoretically. The electrokinetic properties such as volumetric flow rate, total electric current, and streaming potential of the system under consideration are evaluated. The influences of the key parameters, which include the frictional coefficient of the membrane layer, membrane thickness, ionic strength, valence of counterions, fixed charge concentration, and sizes of cations and anions, are discussed. We demonstrate the importance of the steric ionic effects by showing that a substantial difference between the classic point-charge model and the present model.