  We investigated the behavior of an open isotropic universe generated by a
scalar field which couples with background curvature nonminimally with the
coupling constant $\xi$. In particular we focus on the situation where the
initial value for the scalar field $\phi_{\rm in}$ is greater than the critical
value ${\hat \phi}_c$=${m_p}/{\sqrt{8\pi\xi(1-6\xi)}}$. The behavior is similar
to an open de Sitter universe with $k=-1$ with a negative cosmological constant
$\Lambda <0$. It is found that the universe will collapse eventually to a
singularity and thus has a finite extent in time in the future. Furthermore,
there are some cases which shows a rebouncing behavior before the final
collapse.
