The plasmons in graphene and phonon polaritons in hyperbolic materials provide a new approach to mediate near-field radiative heat transfer (NFRHT). This work studies the NFRHT between graphene covered biaxial hyperbolic crystal α-MoO3. The numerical results show that the coupling between plasmons in graphene and phonon polaritons in α-MoO3 can greatly enhance the total heat flux. The spectral heat flux in the Reststrahlen bands can be suppressed or enhanced, depending on the value of the chemical potential of the graphene. What is perhaps most important here is that it is found that the surface plasmon-phonon polaritons can either enhance or suppress the heat transfer, which has not been reported in previous studies. The findings in this work can deepen our understanding of the coupling between graphene plasmons and phonon polaritons in hyperbolic materials.