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We consider the non-local operator of variable order as follows  $$Lf(x)= \int_{\R^d\setminus\{0\}}\big(f(x+z)-f(x)-\<\nabla f(x),z\>  \I_{\{|z|\le 1\}}\big)\frac{n(x,z)}{|z|^{d+\alpha(x)}}\,dz.$$ Under mildconditions on $\alpha(x)$ and $n(x,z)$, we establish the H\"{o}lder regularityfor the associated semigroups. The proof is based on the probabilistic couplingmethod, and it successfully applies to both stable-like processes in the senseof Bass and time-change of symmetric stable processes.

Uniform H\"{o}lder Estimates on Semigroups Generated by Non-Local Operators of Variable Order