We study nonlinear far-field propagation of Kerr spatial solitons along a graphene monolayer embedded planar dielectric waveguide. The volumetric permittivity approach model of graphene is introduced to incorporate this carbon atoms layer into our optical simulations, which mathematically approximate graphene by a very thin layer with a finite thickness. A remarkably large third-order nonlinear optical susceptibility of graphene measured in previous experiment is considered in the numerical simulations. We demonstrate numerically that the TE-polarized beam forms Kerr spatial solitons at high beam intensity, due to the nonlinearity of graphene compensates diffraction losses. It’s very interesting that the Kerr optical solitons can adjust the beam width when propagating to become narrower. We suppose that it’s the selfregulation of the solitons after separating a portion of energy during the transmission process to become more compact. Our simulation results also reveal that the optical field distribution of Kerr optical solitons exhibits obvious periodic oscillation along the propagating path. This is a novel phenomenon that the dynamic regulation of the light field causes spatial oscillation of the solitons and a periodic change in the effective refractive index of graphene monolayer, forming a Kerr-induced index grating in the waveguide. We emphasize that the spatial oscillation of the solitons is due to the dynamic regulation of the light field, with a process of alternating self-focusing and defocusing. We predicate that the transmittance will be improved due to the nonlinear phase modulation by the Kerr-induced index grating through the waveguide.