  We have studied the decay constants of the pseudoscalar and the vector $B$
and $D$ mesons in the framework of the light-cone quark model. We have applied
a variational method to the relativistic Hamiltonian with the Gaussian-type
trial wave function to obtain the values of the scale parameter $\beta$ in
different potential models. Furthermore, using the known values of the
constituent quark masses of $u$, $d$, $s$, $c$ and $b$ quarks, we have obtained
the numerical results for the decay constants. We have also compared our
results with the other theoretical calculations and the existing experimental
results. The present work predictions have many phenomenological applications
in the domain of $CP$ violation and also in the determination of the CKM matrix
elements.
