The magnetoresistance of granular La0.7Ca0.3MnO3 is studied experimentally over wide ranges of temperatures and magnetic fields. The emphasis is on anomalously large hysteresis of magnetoresistance at low temperatures (T = 4.2 K). The observed ρ(H) dependence can be qualitatively explained by spin-dependent tunneling of electrons through the dielectric boundaries of conducting granules characterized by a wide spread in the magnetic-moment magnitudes.