Let \(\Omega\) be a bounded smooth pseudoconvex domain in \({\mathbb C}^n\). For \(\varepsilon>0\), denote by \(\Omega_\varepsilon=\{z\in {\mathbb C}^n: {\text{dist}}(z,\overline\Omega)0\) is small enough, \(\Omega_\varepsilon\) is also smooth. Moreover, if \(\vec n(z)\) denotes the (real) outward unit normal to \(\partial\Omega\), then \(\partial\Omega_\varepsilon=\{z+\varepsilon\vec n(z): z\in\partial\Omega\}\). In this paper, the author proves the following theorem. Theorem. Let \(\Omega\) be a smooth bounded pseudoconvex domain in \({\mathbb C}^n\). Assume there is a function \(\rho(\varepsilon)\) with \(1-\rho(\varepsilon)=o(\varepsilon^2)\) as \(\varepsilon\rightarrow 0^+\) such that, for \(\varepsilon\) small enough, there exists a pseudoconvex domain \(\widetilde \Omega_\varepsilon\) with \(\Omega_{\rho(\varepsilon)\varepsilon} \subseteq\widetilde\Omega_\varepsilon \subseteq \Omega_\varepsilon\). Then the \(\overline\partial\)-Neumann operators \(N_q\) are continuous on the Sobolev space \(W^s_{(0,q)}(\Omega)\), for all \(s\geq 0\) and \(1\leq q\leq n\).