Despite graphene being an attractive transparent conductive electrode for semiconductor deep ultraviolet (UV) light emitting diodes (LEDs), there have been no experimental demonstrations of any kind of semiconductor deep UV LEDs using a graphene electrode. Moreover, although aluminum gallium nitride (AlGaN) alloys in the format of nanowires are an appealing platform for surface-emitting vertical semiconductor deep UV LEDs, in particular, at short wavelengths, there are few demonstrations of AlGaN nanowire UV LEDs with a graphene electrode. In this work, we show that transferred graphene can serve as the top electrode for AlGaN nanowire deep UV LEDs, and devices emitting down to around 240 nm are demonstrated. Compared to using metal, graphene improves both the light output power and external quantum efficiency. Nonetheless, devices with a graphene electrode show a more severe efficiency droop compared to devices with metal. Here, we attribute the heating effect associated with the large contact resistance to be the major reason for the severe efficiency droop in the devices with a graphene electrode. Detailed scanning electron microscopy and Raman scattering experiments suggest that the nanowire height nonuniformity is the main cause for the large contact resistance; this issue could be potentially alleviated by using nanowires grown by selective area epitaxy that is able to produce nanowires with uniform height. This work, therefore, not only demonstrates the shortest wavelength LEDs using a graphene electrode but also provides a viable path for surface-emitting vertical semiconductor deep UV LEDs at short wavelengths.