We design tunable waveguide bends filled with graphene-based anisotropic metamaterials to achieve a nearly perfect bending effect. The anisotropic properties of the metamaterials can be described by the effective medium theory. The nearly perfect bending effect is demonstrated by finite element simulations of various structures with different bending curvatures and shapes. This effect is attributed to zero effective permittivity along the direction of propagation and matched effective impedance at the interfaces between the bending part and the dielectric waveguides. We envisage that the design will be applicable in the far-infrared and terahertz frequency ranges owing to the tunable dielectric responses of graphene.