The present invention relates to a process for modifying the physical and chemical properties of Faujasite Y-type zeolites (FAU), mainly used as a base material of catalyst used in the Fluid Catalytic Cracking (FCC) process, for the interest of the oil refining industry, in which the conversion of oil heavy fractions into lighter fractions, with a higher commercial value, is carried out. The process produces a modified Faujasite Y-type zeolite, with lower sodium content, as low as 75%, than that of the starting Faujasite Y-type zeolite. A mesoporous material associated with the modified Faujasite Y-type zeolite has an average pore size ranging from 2 to 100 nm, having a bimodal or multimodal pore size distribution. The proportion of modified Faujasite Y-type zeolite with respect to the meso-porous material associated to the Faujasite Y type Zeolite can be regulated through the process operation conditions.