  In this paper, the Bosonic projected variational method is proposed to study
the strongly correlated $^{87}{\rm Rb}$ atoms in optical lattice. A global
phase diagram is obtained by this method. There exist two characteristic
lattice depths $V$ for $^{87}{\rm Rb}$ atoms in optical lattice : one is $%
V=9.5E_r$ to label the maximum height of the 'zero-momentum' peak of
condensation, the other is the quantum critical point for the
superfluid-insulator (SI) transition at $V=12.3E_r$. As a result of strongly
correlated effect for lattice Bosons, the suppressed superfluid state is
predicted near the SI transition with the suppressed superfluid density and the
very slowly velocity of the sound-like excitons.
