  In this paper, we firstly verify that if $M$ is a complete self-shrinker with
polynomial volume growth in $\mathbb{R}^{n+1}$, and if the squared norm of the
second fundamental form of $M$ satisfies $0\leq|A|^2-1\leq\frac{1}{18}$, then
$|A|^2\equiv1$ and $M$ is a round sphere or a cylinder. More generally, let $M$
be a complete $\lambda$-hypersurface with polynomial volume growth in
$\mathbb{R}^{n+1}$ with $\lambda\neq0$. Then we prove that there exists an
positive constant $\gamma$, such that if $|\lambda|\leq\gamma$ and the squared
norm of the second fundamental form of $M$ satisfies
$0\leq|A|^2-\beta_\lambda\leq\frac{1}{18}$, then $|A|^2\equiv \beta_\lambda$,
$\lambda>0$ and $M$ is a cylinder. Here
$\beta_\lambda=\frac{1}{2}(2+\lambda^2+|\lambda|\sqrt{\lambda^2+4})$.
