Recently, fast alpha-particle-driven kinetic Alfvén waves were investigated by means of a nonlinear turbulent theory, and an analytic expression for the corresponding diffusion coefficient was derived. This diffusion coefficient is introduced in a kinetic alpha-particle transport code based on the solution of a special Fokker-Planck equation by means of a multigroup formalism. The structure of Dα leads to a nonlinear and self-consistent problem. The simulation of realistic International Thermonuclear Experimental Reactor (ITER)-like plasmas by means of a plasma transport code and a description of the anomalous ion and electron transport by the widely accepted Rebut-Lallia model are dealt with. This code is combined with a kinetic alpha-particle transport code to calculate the alpha-particle power deposition profiles to the plasma electrons and the plasma ions. Results are presented for an ignition scenario for ITER-like plasmas. These seem to be the first plasma simulations using a self-consistent alpha-particle transport model. Estimating the effects of anomalous alpha-particle transport is accomplished by repeating each scenario switching off the alpha-particle transport routine and assuming local alpha-particle power deposition. Important physical quantities like density profiles and diffusion coefficients are discussed.