  Based on a single band Hubbard model and the fluctuation exchange
approximation, the effective mass and the energy band renormalization in
Na$_{0.33}$CoO$_2$ is elaborated. The renormalization is observed to exhibit
certain kind of anisotropy, which agrees qualitatively with the angle-resolved
photoemission spectroscopy (ARPES) measurements. Moreover, the spectral
function and density of states (DOS) in the normal state are calculated, with a
weak pseudogap behavior being seen, which is explained as a result of the
strong Coulomb correlations. Our results suggest that the large Fermi surface
(FS) associated with the $a_{1g}$ band plays likely a central role in the
charge dynamics.
