The magnetic transport properties in granular perovskite system La1-xSrxMnO3 have been investigated. The spin-dependent interfacial tunneling and the corresponding giant magnetoresistance (GMR) effect have been observed in the whole region of temperature below the Curie point T-c for the samples with concentration x from 0.05 to 0.45. Theoretical analysis shows that the interfacial tunneling originates from the difference in magnetism between the grain surfaces and the cores, and the tunnel-type GMR stems from the field-induced change of interfacial magnetic order.