Display omitted •Hydrocracking catalyst activity depends on concentration of Bronsted acid sites (BAS).•Catalyst selectivity depends on BAS concentration in meso- and micropores.•NiMo/small crystals BEA has the highest activity and selectivity to naphtha and gas.•NiMo/small crystals Y has the highest selectivity to diesel. Hydrocracking of vacuum gas oil has been studied over NiMo/zeolite-Al2O3 catalysts. Three different zeolites have been used for catalysts preparation: zeolites Beta (BEA) and Y (FAU) having small crystal size and zeolite Y modified by recrystallization (RFAU). HRTEM, low-temperature N2 adsorption, FTIR of adsorbed CO and TPD-NH3 showed that zeolites had different crystal sizes, mesopore volume, strength and concentration of acid sites. Sulfide active component particles have been revealed to be similar in all catalysts by HRTEM and XPS. NiMo/BEA catalyst having zeolite with the smallest average particle size and the highest concentration of Brønsted acid sites (BAS) demonstrated the highest hydrocracking activity. Selectivity to middle distillates decreased in the following order: NiMo/FAU > NiMo/RFAU > NiMo/BEA. This effect is accounted for by optimal zeolite acidity and improved availability of the acid sites for bulky molecules of the heavy feedstock.