The Fermi energy, cyclotron energy and cyclotron effective mass of degenerate electron gas in a size-quantized semiconductor thin film with non-parabolic energy bands are studied. The influences of quantizing magnetic field on these quantities in two-band approximation of the Kane model are investigated. It is shown that the Fermi energy oscillates in a magnetic field. The period and positions of these oscillations are found as a function of film thickness and concentration of electrons. Cyclotron energy and cyclotron effective mass are investigated as a function of film thickness in detail. The results obtained here are compared with experimental data on GaAs quantum wells.