Most of the current graphene plasmonic researches are based on the substrates with isotropic dielectric constant such as silicon.In this work,we investigate optical properties of graphene nanoribbon arrays placed on a uniaxially anisotropic substrate,where the anisotropy provides an additional freedom to tune the behaviors of graphene plasmons,and its effect can be described by a simple effective formula.In practice,the substrates of semi-infinite and finite thickness are discussed by using both the formula and full wave simulations.Particularly,the dielectric constants ε|| and ε⊥ approaching zero are intensively studied,which show different impacts on the transverse magnetic(TM)surface modes.In reality,the hexagonal boron nitride(hBN)can be chosen as the anisotropic substrate,which is also a hyperbolic material in nature.