A kind of surface plasmon waveguide composed of two nested cylindrical dielectric parallel nanowire pairs coated with graphene was designed and studied. The dependence of the mode characteristics and the normalized gradient force of the lowest two modes supported by the waveguide on the parameters involved were analyzed by using the multipole method. To ensure rigor, the finite element method was employed to verify the accuracy of the multipole method, thus confirming its results. The results show that the multipole method is a powerful tool for handling this type of waveguide. The real part of the effective refractive index, the propagation length, the figure of merit, and the normalized gradient force can be significantly affected by the operating wavelength, the Fermi energy of graphene, the waveguide geometric parameters, and the refractive index of the inner dielectric nanowire. Due to the employment of nested dielectric nanowire pairs coated with graphene, this waveguide structure exhibits significant gradient force that surpasses 100 nN·μm−1·mW−1. The observed phenomena can be attributed to the interaction of the field with graphene. This waveguide holds promising potential for applications in micro/nano integration, optical tweezers, and sensing technologies.