Quantum oscillations have long been regarded as the manifestation of the Fermi surface in metals. However, they were recently observed in Kondo insulators. We examine the Kondo screening due to Landau levels in Kondo insulators. It is shown that, even for large Kondo insulating gaps, appreciable amplitudes of quantum oscillations that are consistent with experimental observations are present both in magnetization and resistivity. Specifically, we show that, due to the periodic alignment between the Landau levels in the conduction and the f-orbit electrons, the Kondo screening itself undergoes oscillations so that the electronic structure oscillates with the magnetic field. Our results explain main features of quantum oscillations observed in experiments. They indicate that the nonrigidity of the electronic structure results in observable quantum oscillation Kondo insulators. This effect provides a way to probe the Fermi surface geometry of insulators.