  We study the local linear estimator for the drift coefficient of stochastic
differential equations driven by $\alpha$-stable L\'{e}vy motions observed at
discrete instants letting $T \rightarrow \infty$. Under regular conditions, we
derive the weak consistency and central limit theorem of the estimator. Compare
with Nadaraya-Watson estimator, the local linear estimator has a bias reduction
whether kernel function is symmetric or not under different schemes.
