The resistivity and magnetoresistance of bulk polycrystalline La0.7Sr0.3MnO3(LSM), deliberately fabricated to produce nanoscale grains, has been investigated as functions of temperature. With decreasing temperature below room temperature the resistivity (ρ) exhibits a maximum near 250K， below which it displays a “metallic" behaviour. However, ρ exhibits subsequently a minimum near 50K, below which it is well fit by the predictions for the tunneling of conduction electrons through insulating interfacial layers viz. lnρ∝T-1/2, a result interpreted as conduction-electron tunneling between adjacent LSM granules. The minimum of ρ occurs in this particular sample may result from the competition of the tunneling effect and the intrinsic transport mechanism of LSM. The temperature dependence of the associated tunneling magnetoresistance is also reported in this low temperature regime.