We investigate the phase coherence of bosons in a double-well trap with a random energy mismatch that is used to mimic disorder in the presence of effective three-body interaction. It is found that, in such a double-well disordered Bose-Hubbard model, the renormalized three-body interaction can enhance the phase coherence of the bosonic system in the presence of disorder. The dependence of the average phase coherence on the effective three-body interaction in the situation of strong disorder is also studied. To our best knowledge, it is the first time that the effective three-body interaction is investigated in the context of disordered quantum gases.