  We investigate the inflation of Universe in a model of four dimensional
dilatonic gravity with a massive dilaton field $\Phi$. The dilaton plays
simultaneously the roles of an inflation field and a quintessence field. It
yields a sequential {\em hyper}-inflation with a graceful exit to asymptotic de
Sitter space-time, which is an attractor, and is approached as
$\exp(-\sqrt{3\Lambda^{obs}} ct/2)$. The time duration of the inflation is
reciprocal to the the mass of the dilaton: $\Delta t_{infl}\sim
m_{{}_\Phi}^{-1}$. The typical number of e-folds in the simplest model of this
type is shown to be realistic without fine tuning.
