We propose a theoretical model of magnetic field dependence of hysteretic switching in magnetic granular system. The model is based on the self-trapped electrons mechanism. Our calculations show that the switching voltage may be significantly decreased with increasing the magnetic field. The underlying mechanism is the influence of the magnetic field on electron occupation of the conduction band, which depends on the materials used in magnetic granular system, concentration of magnetic granules in the insulating matrix, applied voltage, and the charge accumulation on the granules. We support our theoretical calculations by measuring the magnetic field dependence of resistive switching behaviour in Co/Al2O3 granular multilayers. Our experimental results are in qualitative agreement with the proposed theory.