  In this paper, we study the complete bounded $\lambda$-hypersurfaces in
weighted volume-preserving mean curvature flow. Firstly, we investigate the
volume comparison theorem of complete bounded $\lambda$-hypersurfaces with
$|A|\leq\alpha$ and get some applications of the volume comparison theorem.
Secondly, we consider the relation among $\lambda$, extrinsic radius $k$,
intrinsic diameter $d$, and dimension $n$ of the complete
$\lambda$-hypersurface, and we obtain some estimates for the intrinsic diameter
and the extrinsic radius. At last, we get some topological properties of the
bounded $\lambda$-hypersurface with some natural and general restrictions.
