It has been considered that the contribution of the vapor-phase reaction (VPR) to the global three-phase reaction rate may become much lower as the catalyst effectiveness factor approaches unity. In this study, the hydrogenation of 1-methylnaphthalene was performed as an example of slow reactions using a laboratory-scale trickle-bed reactor (TBR) at 583 K, 8.0 MPa. It was qualitatively confirmed that VPR contributed to the product yields in TBR even in this slow reaction system when the liquid velocity was low and the volatility of the liquid was high. Langmuir-Hinshelwood type kinetic equations were established for the vapor-phase reaction. The product yields in TBR neither be explained by liquid- vapor-phase kinetics without external effects, nor the conventional partial wetting model. Therefore, a partial wetting model considering the contribution of VPR was proposed where the catalyst bed composed of externally partial and internally complete wet particles, and completely dry particles was assumed. Using this model, the product yields in TBR were suitably explained.