Micro/mesoporous composite materials with different levels of micro- and mesoporosity were prepared by recrystallization of mordenite in the presence of cethyltrimethylammonium bromide. The materials were characterized by XRD, TEM, IR spectroscopy, nitrogen adsorption-desorption and NH3-TPD. The results highlight that recrystallization in mild condition results in the creation of mesopores in the zeolite crystals and their coating with thin films of mesoporous material. The increase of the degree of recrystallization leads first to the formation of composite materials MOR/MCM-41 and then to a complete transformation of mordenite in MCM-41, followed by a gradual decrease of the amount and strength of acid sites. Recrystallized materials display remarkably high activity, stability and selectivity in alkylation of naphthalene with cyclohexene. The effect is due to the improved accessibility of active sites and easier transport of bulky molecules provided by mesopores. The best catalytic performance is achieved on composite materials with intermediate degree of recrystallization. The yield of alkylnaphthalenes over these materials reaches 80%, while the yield of monoalkylnaphthalenes is up to 58%.