There exist two kinds of critical current densities in polycrystalline bulk of MgB2, i.e., the large local critical current density corresponding to the shielding current in inductive measurements, which flows inside the grains, and the small global critical current density that flows through the grains for whole sample. This behavior is considered to be mainly caused by the significant granularity in polycrystalline bulk. In this work, MgB2 superconductors are prepared under different Spark plasma sintering (SPS) heating rates. The microstructures of the samples are investigated, and their critical current densities are measured by Campbell method from the penetrating AC flux profile and the AC magnetic field versus penetration depth. It is found that an extremely high global critical current flows through the whole sample with a bigger grain size, which is prepared by a low heating rate during SPS sintering. That is to say, the grain refinement only increases the local critical current density of the sample. These results imply that the global current is reduced due to the existence of various defects and the poor electrical connectivity in MgB2 sample.