Based on the spin-polarized intergrain tunneling, the origin of temperature-dependent low-field magnetoresistance (MR) is presented for the polycrystalline manganites. In consideration of the spin-flip intergrain tunneling arising from the Mn ion impurities in the grain-boundary regions, it is shown that the variation of the electronic spin polarization and the inelastic intergrain tunneling induced by the collective excitations of local spins at the grain boundaries are simultaneously responsible for the rapid decay of the low-field MR ratio with increasing temperature. The theoretical results are in agreement with the experimental data of the polycrystalline manganites.