Measurements were made of electrical transport properties of the electrons in inversion layers produced in metal–oxide–p-InSb structure at 4.2 K. One possible interpretation is reported. Surface conductance Δσs due to inversion layers as a function of gate voltage VG was measured in magnetic field H up to 14 kOe. The curves of Δσs in the magnetic field normal to the surface had plateaus. The width of the plateaus were enlarged on the positive side of VG with increasing magnetic field. While Δσs in the magnetic field normal to the surface decreased ordinarily with increasing H, Δσs in the field parallel to the surface plane tended to a finite value. Values of Δσs showed two peaks when the direction of the magnetic field was rotated in a plane normal to the surface current. The width of the peak was narrower in the case of magnetic fields where electrons were pushed toward the oxide–InSb interface rather than into the bulk of the InSb. These characteristics may be interpreted as follows: The effect of quantization of electron motion in the inversion layer becomes clearer in the behavior of Δσs with the aid of a magnetic field which quantizes the motion of electrons in planes parallel to surface. The peculiar dependence of Δσs on the direction of the magnetic field is thought to originate in the different mechanisms of electron scattering on both sides of the inversion layers mentioned above.