  The strong coupling constant $g_{\Upsilon B_c^{ps} B_c^V}$ is evaluated using
the three-point QCD sum rules. The correlation functions used to calculate
these strong coupling constants contain contributions of both $B_c^V$ and
$B_c^{ps}$ mesons as off-shell states with contributions of two gluon
condensates as a radiative corrections. The results, $g_{\Upsilon B_c^V
B_c^{PS}}=1.67\pm 0.52 GeV^{-1}$ for $B_c^{Ps}$ off-shell and $g_{\Upsilon
B_c^{PS}B_c^V}=(0.87\pm0.25) GeV^{-1}$ for $B_c^V$ off-shell are obtained for
the relevant strong coupling constants
