The performance of organic semiconductor thin films in electronic devices is related to their crystal structure and morphology, with charge transport mobility dependent on the degree of crystallinity and on the crystallographic orientation. Here organic molecular beam deposition of vanadyl phthalocyanine is studied on graphene and it is shown that crystalline grains up to several micrometers across can be formed at substrate temperatures of 155 degrees C, compared to room temperature grain sizes of approximate to 30 nm. Transmission electron microscopy confirms the presence of long range order at elevated substrate temperatures and reveals that the molecules are stacked in an edge-on orientation, but are not epitaxially aligned to the graphene. The crystalline grain sizes are significantly larger on graphene than on disordered substrates such as graphene oxide and silicon oxide. The effect on charge transport is probed by conducting atomic force microscopy, with the high temperature films on graphene showing increased mobility and uniformity and decreased trap density. These results illustrate an important advantage for the integration of graphene electrodes with organic semiconductor devices: the homogeneous surface of graphene results in high diffusion and low nucleation rates for thin film growth, encouraging the formation of highly crystalline films even with nonepitaxial growth.