  In this paper, we study complete hypersurfaces with constant mean curvature
in anti-de Sitter space $H^{n+1}_1(-1)$. we prove that if a complete space-like
hypersurface with constant mean curvature $x:\mathbf M\rightarrow H^{n+1}_1(-1)
$ has two distinct principal curvatures $\lambda,\mu$, and
inf$|\lambda-\mu|>0$, then $x$ is the standard embedding $ H^{m}
(-\frac{1}{r^2})\times H^{n-m} (-\frac{1}{1 - r^2})$in anti-de Sitter space $
H^{n+1}_1 (-1)$.
