This article considers the system, which is described by a nonlinear differential equation with the Hukuhara derivative with a control parameter with rapidly fluctuating coefficients. The possibility of using the averaging method is substantiated for this system. The main resultsof this work is the theorem about closeness of solutions original equation and averaged one with the same control function, and the theorem about the convergence of the solutions of the original problem to the optimal solutions of the averaged problem: on the convergence of optimal controls of the original problem to optimal controls of the averaged problem, on the convergence of the trajectories of the exact problem to the trajectories of the averaged problem, on the closeness of the criteria values of the original and averaged problems.