Graphene plasmons, owing to their diverse applications including electro-optical modulation, optical sensing, spectral photometry and tunable lighting at the nanoscale, have recently attracted much attention. One key challenge in advancing this field is to precisely control the propagation of graphene plasmons. Here, we propose an on-chip integrated platform to engineer the wave front of the graphene plasmons through a metasurface with a refractive index of zero. We demonstrate that a well-designed graphene/photonic-crystal metasurface can possess conical plasmonic dispersion at the Brillouin zone center with a triply degenerate state at the Dirac frequency, giving rise to the zero-effective-index of graphene plasmons. Plane-wave-emission and focusing effects of the graphene plasmons are achieved by tailoring such a zero-index metasurface. In addition to the tunable Dirac point frequency enabled by the electrical tuning of the graphene Fermi level, our highly integrated system also provides stable performance even when defects exist. This actively controllable on-chip platform can potentially be useful for integrated photonic circuits and devices.