||We have numerically studied the magnetoresistance of granular metal-insulator materials in the nearest-neighbor hopping (NNH) regime, in which the tunneling between two nearest neighbor clusters is the main transport mechanism. The aim of our works is to propose a level-shifting mechanism to explain the negative magnetoresistance (NMR). Under this mechanism, we can find and explain most of the characteristics of NMR in NNH regime observed in experiments. We have shown that hopping current increases with the strength of magnetic field when the cluster-cluster distance is small and at low enough temperature. These results agree with the recent experiments which show the NMR near the percolation threshold in granular materials. The temperature dependence of NMR in experiments is also agrees with our calculation. Moreover, the mechanism can explain naturally why the NMR is not observed in granular material when the metallic grain size is very small. We point out that the magnetic field affect the tunneling matrix element between two states of two grains in three important ways. They are the gauge factor effect, shrinking effect and the level shifting effect. We conclude that level shifting effect is the source of NMR. However, the sign of the magnetoresistance still depend on the competition of the three effects.