  In this paper, we study the averaging principle for a class of stochastic
differential equations driven by $\alpha$-stable processes with slow and fast
time-scales, where $\alpha\in(1,2)$. We prove that the strong and weak
convergence order are $1-1/\alpha$ and $1$ respectively. We show, by a simple
example, that $1-1/\alpha$ is the optimal strong convergence rate.
