The isolation of graphene on an insulating substrate has provided new opportunities for the fabrication of electronic devices with radically new geometries and structures. The use of single-layer graphene as an electrode has enabled the development of novel electronic device architectures that exploit the unique atomically thin structure of the material, which also includes a low density of states at its charge neutrality point. In this work, we present the first example of a vertical Schottky junction photodiode based on the graphene.organic semiconductor.metal heterostructure. The n-type N,N0-dioctyl-3,4,9,10-perylenedicarboximide (PTCDI-C8) organic semiconductor was thermally deposited onto chemical vapor deposition (CVD)-grown single-layer graphene. The tunable Schottky injection barrier permitted tuning of the diode rectification ratio by more than two orders of magnitude upon application of gate biases, which increased the photocurrent but suppressed the dark current of the photodiodes. Tuning of the photovoltaic properties of the devices was also confirmed, indicating that the device architecture based on the work function tunability of graphene could provide a versatile strategy for enhancing the performance of organic photodiodes.