A new decoration method is proposed which can achieve an exact mapping between the quenched bond randomly diluted spin-1 Ising model on a regular lattice in the subspace: exp(K)cosh (J) =1 and a certain class of mixed-spin quenched site randomly diluted decorated-lattice problem. Using this mapping in conjunction with the annealed model solution for the decorated-lattice problem, we have obtained the approximate results for the quenched bond randomly diluted spin-1 Ising model on the honeycomb lattice. The critical temperature and the magnetization of the diluted system as functions of bond concentration are calculated in detail.