We propose a waveguide based on three graphene-coated dielectric nanowires with a non-coplanar axis using the multipole method, and analyze the real part of effective refractive index and propagation length of five supported low-order modes by changing the operating frequency, radius and height of the central nanowires, the horizontal space between the nanowires, and the Fermi energy of graphene. When the operating frequency increases from 30 THz to 40 THz, the real part of the effective refractive index increases, whereas the propagation length decreases. When the radius of the central nanowire increases from 20 nm to 55 nm, the real part of effective refractive index increases; however, the corresponding propagation length varies. When the height of the central nanowire increases from 0 to 100 nm, the real part of effective refractive index decreases, whereas the propagation length increases, except for that of mode 5. When the horizontal space between the nanowires increases from 160 nm to 200 nm or the Fermi energy increases from 0.4 eV to 0.8 eV, the propagation length increases, whereas the real part of the effective refractive index decreases.