  In this paper we develop the compactness theorem for $\lambda$-surface in
$\mathbb R^3$ with uniform $\lambda$, genus, and area growth. This theorem can
be viewed as a generalization of Colding-Minicozzi's compactness theorem for
self-shrinkers in $\mathbb R^3$. As an application of this compactness theorem,
we prove a rigidity theorem for convex $\lambda$-surfaces.
