We will study the convergence rate of SDE driven by $\alpha$-stable process as $\alpha \rightarrow 2$ and prove that the rate is $(2-\alpha) |log(2-\alpha)|$ in Wasserstein distance. This rate is optimal up to a correction $\log (2-\alpha)$. The method is by a discretization and the Lindeberg principle developed by Chen, Shao and Xu. This is a joint work in progress with Changsong Deng (Wuhan University) and Rene Schilling.