  Considering the fact that, a wide range of variation in masses of various
states of heavy pseudoscalar and vector mesons can be seen in different models
and the experimental data on masses of many of these states is not yet
currently available, in this paper, we study the analytical calculation of
heavy pseudoscalar and vector mesons mass spectra ( such as $\eta_{c}$,
$B_{c}$, $\eta_{b}$, $J/\psi$, $B^{*}_{c}$ and $\Upsilon$) and their
corresponding wave functions in the framework of Bethe-Salpeter equation under
the covariant instantaneous ansatz. The parameters of the framework were
determined by a fit to the heavy pseudoscalar and vector mesons mass spectrum
of ground states. These input parameters so fixed were found to give good
agreements with data on mass spectra of ground and excited states of these
mesons mass spectra.
