The strong coupling constant grB(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, grB(c)(V)B(c)(PS) = 1.67 +/- 0.52 GeV-1 for B-c(Ps) off-shell and grB(c)(PS) B-c(V) = (0.87 +/- 0.25) GeV-1 for B-c(V) off-shell are obtained for the relevant strong coupling constants.