Carbon impurity as point defects makes key impact on the leakage in GaN-on-Si structures. GaN-based epitaxial layers with different point defects by changing carbon-doped concentration were used to investigate the point defects behavior. It was found that leakage mechanisms correspond with space-charge-limited current models at low voltages, and after 1st kink, electron injection from silicon to GaN and PF conduction play a key role in the leakage of both point defects case with low carbon and high carbon doped. In addition, high carbon in GaN-on-Si epitaxial layers obtained lower leakage and larger breakdown voltage. The slope of log J-V has two kinks and effective energy barrier Ea has two peaks, 0.4247eV at about 300V and 0.3485eV at about 900V, respectively, which is related to accepted states and donor states related with carbon impurity. While the slope of log J-V has one kink and effective energy barrier Ea has one peak, 0.4794eV at about 400V of low carbon in GaN-on-Si epitaxial layers, indicating only Field-induced accepted ionized makes impact on leakage. The comparative results of more donor trap density in high carbon indicate point defects related with carbon impurity play a key role in the kinks of log J-V slope.