  The energy spectrum for the three dimensional Bose gas in Bose-Einstein
Condensation phase is calculated with Modified Hartree-Fock-Bogoliubov theory,
which is both conserving and gapless. From Improved $\Phi -$% derivable theory,
the diagrams needed to preserve Ward-Takahashi Identity are resummed in a
systematic and nonperturbative way. The results show significant discrepancies
with Popov theory at finite temperature. It is valid up to the critical
temperature where the dispersion relation of the low energy excitation spectrum
changes from linear to quadratic. Because of the repulsive interaction, the
critical temperature has a positive shift from that of idea gas, which is in
accordance with the result from the previous calculations in the uncondensed
phase.
