Pristine graphene and a graphene interlayer inserted between indium tin oxide (ITO) and p-GaN have been analyzed and compared with ITO, which is a typical current spreading layer in lateral GaN LEDs. Beyond a certain current injection, the pristine graphene current spreading layer (CSL) malfunctioned due to Joule heat that originated from the high sheet resistance and low work function of the CSL. However, by combining the graphene and the ITO to improve the sheet resistance, it was found to be possible to solve the malfunctioning phenomenon. Moreover, the light output power of an LED with a graphene interlayer was stronger than that of an LED using ITO or graphene CSL. We were able to identify that the improvement originated from the enhanced current spreading by inspecting the contact and conducting the simulation.