We present a study of the magnetoresistance and Hall effect in the narrow-gap semiconductor FeSb2 at low temperatures. Both the electrical and Hall resistivities show unusual magnetic field dependence in the low-temperature range where a large Seebeck coefficient was observed. By applying a two-carrier model, we find that the carrier concentration decreases from 1 down to 10^-4 ppm/unit cell and the mobility increases from 2000 to 28000 cm2/Vs with decreasing temperature from 30 down to 4 K. At lower temperatures, the magnetoresistive behavior drastically changes and a negative magnetoresistance is observed at 3 K. These low-temperature behaviors are reminiscent of the low-temperature magnetotransport observed in doped semiconductors such as As-doped Ge, which is well described by a weak-localization picture. We argue a detailed electronic structure in FeSb2 inferred from our observations. ; Comment: 5 pages, 5 figures, to be published in Phys. Rev. B