In the light of the effective-field theory, the present paper attempts to discuss the investigation done into the phase diagrams of a random nearest-neighbour interaction spin-1 Ising model with a single-ion anisotropy in an applied transverse field on the honeycomb lattice. The interactions are assumed to be independent random variables with distribution P(J_ij)=p delta (J_ij-J₁)+(1-p) delta (J_ij-J₂), where J₁>0and mod J₂/J₁ mod <or=1. We find a number of interesting phenomena, such as two different types of re-entrant phenomenon due to the competition between the random bond and the negative single-ion anisotropy parameter, as well as the usual frustration of J_ij. The influence of a transverse field on the behaviours of the tricritical point and re-entrant transition is also discussed in this paper.