In this paper, it is shown that in the n-InSb/YIG/GGG (YIG is yttrium iron garnet, GGG is gadolinium gallium garnet) structure, when the geometry of magnetization is tangential to the substrate plane (H < 10 kOe) and temperature T approximate to 300 K, the effect of negative magnetoresistance of about 1% appears, whereas in the n-InSb/GGG structure with the same geometry of magnetization, the magnetoresistance is positive (increase in electrical resistance in the magnetic field). The effect of negative magnetoresistance in the InSb/YIG/GGG structure is stipulated by the effect of the YIG magnetization on the conduction electrons of InSb (proximity effect) with the impact value determined by the YIG magnetization value and the InSb film parameters.