Summary: The large time behavior of solutions of the Cauchy problem for the one-dimensional fractal Burgers equation \(u_t+(-\partial^2_x)^{\alpha/2} u+uu_x=0\) with \(\alpha\in (1,2)\) is studied. It is shown that if the nondecreasing initial datum approaches the constant states \(u_\pm (u_-<u_+)\) as \(x\to \pm\infty\), respectively, then the corresponding solution converges toward the rarefaction wave, i.e., the unique entropy solution of the Riemann problem for the nonviscous Burgers equation.