Epitaxial graphene thermally grown on 6H-SiC(0001) can be p-type doped via a novel surface transfer doping scheme by modifying the surface with the electron acceptor, tetrafluoro-tetracyanoquinodimethane (F4-TCNQ). Synchrotron-based high-resolution photoemission spectroscopy reveals that electron transfer from graphene to adsorbed F4-TCNQ is responsible for the p-type doping of graphene. This novel surface transfer doping scheme by surface modification with appropriate molecular acceptors represents a simple and effective method to nondestructively dope epitaxial graphene for future nanoelectronics applications.