Bi-functional catalysts were prepared using HY zeolites with various SiO2/Al2O3 ratios for acidic function, NiW for metallic function, and K for acidity control. 1-Methylnaphthalene was selected as a model compound for multi-ring aromatics in heavy oil, and its selective ring opening reaction was investigated using the prepared bi-functional catalysts with different levels of acidity in a fixed bed reactor system. In NiW/HY catalysts without K addition, the acidity decreased with the SiO2/Al2O3 mole ratio of the HY zeolite. Ni1.1W1.1/HY(12) catalyst showed the highest acidity but slightly lower yields for the selective ring opening than Ni1.1W1.1/HY(30) catalyst. The acidity of the catalyst seemed to play an important role as the active site for the selective ring opening of 1-methylnaphthalene but there should be some optimum catalyst acidity for the reaction. Catalyst acidity could be controlled between Ni1.1W1.1/HY(12) and Ni1.1W1.1/HY(30) by adding a moderate amount of K to Ni1.1W1.1/HY(12) catalyst. K0.3Ni1.1W1.1/HY(12) catalyst should have the optimum acidity for the selective ring opening. The addition of a moderate amount of K to the NiW/HY catalyst must improve the catalytic performance due to the optimization of catalyst acidity.