  A self-consistent theory is derived to describe the BCS-BEC crossover for a
strongly interacting Fermi gas with a Feshbach resonance. In the theory the
fluctuation of the dressed molecules, consisting of both preformed Cooper-pairs
and ``bare'' Feshbach molecules, has been included within a self-consistent
$T$-matrix approximation, beyond the Nozi\`{e}res and Schmitt-Rink strategy
considered by Ohashi and Griffin. The resulting self-consistent equations are
solved numerically to investigate the normal state properties of the crossover
at various resonance widths. It is found that the superfluid transition
temperature $T_c$ increases monotonically at all widths as the effective
interaction between atoms becomes more attractive. Furthermore, a residue
factor $Z_m$ of the molecule's Green function and a complex effective mass have
been determined, to characterize the fraction and lifetime of Feshbach
molecules at $T_c$. Our many-body calculations of $Z_m$ agree qualitatively
well with the recent measurments on the gas of $^6$Li atoms near the broad
resonance at 834 Gauss. The crossover from narrow to broad resonances has also
been studied.
