It is known that threading dislocations degrade the performance of GaN-based electronic devices. Electronic structure of threading dislocations in GaN is not fully understood. Accordingly, we examine the electronic structures of threading dislocations in GaN using first principles calculations based on density functional theory (DFT) and to clarify the origin of the leakage current. We have comprehensively studied the relation between threading core structures and electronic property in GaN thin films. Our calculation models of threading dislocations are the edge dislocations with Burgers vectors of 1/3 [11-20] and the screw dislocations with Burgers vectors of . We examined various core types of the threading dislocations. We found that both edge dislocations and screw dislocations do not cause the leakage currents in n-type GaN based devices because no defect level appears near the conduction band bottom.