  As we all known that non-relativistic or semi-relativistic constituent quark
models can describe a large number of the meson sand baryon properties with
surprising accuracy. In this work, we studied Killingbeck potential by using
WKB approximation in the constituent quark model. The implicit approximate
solution of the energy eigenvalue of the Schr\"{o}dinger equation is obtained
by using appropriate quantization conditions. Under the Killingbeck potential
with the WKB approximation, we studied the spectra of double heavy mesons and
predict the masses of high excited states in $c\bar{c}$, $b\bar{b}$ and
$b\bar{c}$ families. Finally, we discuss the application scope of double heavy
mesons in Killingbeck potential.
