Advanced materials that combine novel functionality and ease of applicability are central to the development of light-emitting diodes (LEDs), which is of ever increasing commercial importance. Here a new metal-insulator-semiconductor (MIS) LED structure that combines economical fabrication with novel device properties is reported. The presented MIS-LED consists of a graphene electrode on p-GaN substrate separated by an insulating SiO2 layer. It is found that the MIS-LED possesses a unique tunability of the electroluminescence spectra depending on the bias conditions. Tunnel injection from graphene into the p-GaN can explain the difference in luminescence spectra under forward and reverse bias. The demonstrated MIS-LED expands the use of graphene and also possibly allows the direct integration of light emitters with other circuit elements.