  The strong coupling constant g$_{h_{b}B_{c}^{PS}B_{c}^{V}}$ is calculated
using the three-point QCD sum rules method. We use correlation functions to
obtain these strong coupling constants with contributions of both B$_{c}^{PS} $
and B$_{c}^{V}$mesons as off-shell states. The contributions of two gluon
condensates as a radiative correction are considered. The results show that
g$_{h_{b}B_{c}^{PS}B_{c}^{V}}=8.80\pm 2.84 GeV^{-1}$and g$_{h_{b}B_{c}^{V}
B_{c}^{PS}}=9.34\pm 3.12 GeV^{-1}$ in the $B_{c}^{PS}$ and $B_{c}^{V}$
off-shell state, respectively.
