Liquid phase isopropylation of biphenyl with propylene was studied over a cerium exchanged sodium mordenite (Ce/NaM25) and a H-mordenite (HM25) with the same SiO2/Al2O3 ratio of 25. Shape-selective catalysis occurred to give 4,4’-diisopropylbiphenyl (4,4’-DIPB) in high selectivity over Ce/NaM25 under any propylene pressures. HM25 gave 4,4’-DIPB shape-selectively under high propylene pressures. However, the reaction was severely deactivated at a conversion of ca. 60% under such a low pressure as 0.8 kg/cm2 because of coke formation in the pore. The yeilds of 4-isopropylbiphenyl (4-IPBP) and 4,4’-DIPB decreased with the increase of those of 3-IPBP and 3,4’-DIPB because of non-selective alkylation and isomerization at external acid sites that are alive in spite of severe deactivation. No significant isomerization of 4,4’-DIPB over Ce/NaM25 was observed even at low propylene pressure. In the case of HM25, the isomerization of 4,4’-DIPB to 3,4’-DIPB occurred significantly under low propylene pressures, while it decreased under high pressure. These differences are ascribed to the differences of nature of acid sites between Ce/NaM25 and HM25 zeolites.