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We establish the exponential convergence with respect to the$L^1$-Wasserstein distance and the total variation for the semigroupcorresponding to the stochastic differential equation (SDE)  $$d X_t=d Z_t+b(X_t)\,d t,$$ where $(Z_t)_{t\ge0}$ is a pure jump L\'{e}vyprocess whose L\'{e}vy measure $\nu$ fulfills  $$ \inf_{x\in \R^d, |x|\le \kappa_0} [\nu\wedge (\delta_x \ast \nu)](\R^d)>0$$ for some constant $\kappa_0>0$, and the drift term $b$ satisfies thatfor any $x,y\in \R^d$,  $$\langle b(x)-b(y),x-y\rangle\le \begin{cases}  \Phi_1(|x-y|)|x-y|,& |x-y|\le l_0;  -K_2|x-y|^2,& |x-y|> l_0  \end{cases}$$ with some positive constants $K_2, l_0$ and positive measurablefunction $\Phi_1$. The method is based on the refined basic coupling forL\'{e}vy jump processes. As a byproduct, we obtain sufficient conditions forthe strong ergodicity of the process $(X_t)_{t\ge0}$.

Refined basic couplings and Wasserstein-type distances for SDEs with L\'{e}vy noises