Owing to a high electromagnetic confinement and a strong photonic density of states, hyperbolic surface plasmon polaritons (HSPPs) provide a fascinating promise for applications in thermal photonics. In this work, we theoretically predict a possibility for the improvement of the near-field radiative heat transfer on the basis of tailoring the electromagnetic state of hyperbolic metasurfaces by the uniaxial hyperbolic substrate. By using the photonic tunneling coefficient and the polaritons dispersion, we present a comprehensive study of the hybrid effect of the hyperbolic substrate on HSPPs. We find that due to the hybrid effect of the hyperbolic substrate, the anisotropy surface state of hyperbolic metasurfaces would undergo significant deformations and even topological transition. Moreover, we systematically exhibit the evolution of such hybrid hyperbolic mode with different thicknesses of the hyperbolic substrate and analyze the thickness effect on radiative properties of the hybrid system. It is shown that the resulting heat transfer with the assistance of the hybrid hyperbolic mode by optimizing the substrate parameters is many times stronger than that of monolayer hyperbolic metasurface at the same vacuum gap. Taken together, our results provide a platform to tailor 2D hyperbolic plasmons as a potential strategy toward passive or active control of the near-field heat transfer, and the hybrid hyperbolic mode presented here may facilitate the system design for near-field energy harvesting, thermal imaging, and radiative cooling applications.