  In this article, we obtain the rates of convergence for superdiffusion in the
Boltzmann-Grad limit of the periodic Lorentz gas, which is one of the
fundamental models to study diffusions in deterministic systems. In their
seminal work, Marklof and Str\"ombergsson proved the Boltzmann-Grad limit of
the periodic Lorentz gas~\cite{M-Sannals2}, and then Marklof and T\'oth
established a superdiffusive central limit theorem in large time for the
Boltzmann-Grad limit~\cite{M-T16}. Based on their work, we apply Stein's method
to derive the convergence rates for the superdiffusion in the Boltzmann-Grad
limit of the periodic Lorentz gas. For the discrete time displacement the rate
of convergence in Wasserstein distance is obtained, while in the context of the
continuous time displacement the result is presented for the Berry-Essen type
bound.
