  We report that the {\pi}-electrons of graphene can be spin-polarized to
create a phase with a significant spin-orbit gap at the Dirac point (DP) using
a graphene-interfaced topological insulator hybrid material. We have grown
epitaxial Bi2Te2Se (BTS) films on a chemical vapor deposition (CVD) graphene.
We observe two linear surface bands both from the CVD graphene notably
flattened and BTS coexisting with their DPs separated by 0.53 eV in the
photoemission data measured with synchrotron photons. We further demonstrate
that the separation between the two DPs, {\Delta}D-D, can be artificially
fine-tuned by adjusting the amount of Cs atoms adsorbed on the graphene to a
value as small as {\Delta}D-D = 0.12 eV to find any proximity effect induced by
the DPs. Our density functional theory calculation shows a spin-orbit gap of
~20 meV in the {\pi}-band enhanced by three orders of magnitude from that of a
pristine graphene, and a concomitant phase transition from a semi-metallic to a
quantum spin Hall phase when {\Delta}D-D $\leq$ 0.20 eV. We thus present a
practical means of spin-polarizing the {\pi}-band of graphene, which can be
pivotal to advance the graphene-based spintronics.
