Summary: The anomalous diffusion due to accelerator-mode islands in the standard map is analyzed with the aid of Tsallis nonextensive statistics. In this treatment, we introduce a new variable \(x\), which represents the displacement per jump while the chaotic orbit is trapped by the accelerator-mode islands. We have shown numerically that the one-jump distribution function \(p(x)\) is qualitatively similar to the function \(p_q(x)\) derived using the maximum Tsallis entropy principle with appropriate conditions [C. Tsallis, J. Stat. Phys. 52, No. 1–2, 479–487 (1988; Zbl 1082.82501); Phys. Lett. A 195, No. 5–6, 329–334 (1994; Zbl 0941.81565)] We find that the \(n\)-jump distribution function \(p(x,n)\) converges to the \(n\)-jump distribution function \(p_q(x,n)= \frac{1}{n^{1/\gamma}} p_q (\frac{x}{n^{1/\gamma}})\) obtained from the Lévy-Gnedenko central-limit theorem in the \(n\to\infty\) limit.