To obtain a catalyst having improved catalytic performance, especially selectivity in the disproportionation reaction of alkyl arom. hydrocarbon and/or the trans-alkylation reaction of alkyl arom. hydrocarbon.

This catalyst contains mazzite structure type zeolite preferably zeolite omega. The zeolite contains at least one (T) of gallium and aluminum, preferably aluminum and silicon, the atomic ratio of Si to T in the entire zeolite is 5-100, preferably 6-80, especially preferably 8-60 and the number of T atoms at the outside of the lattice is smaller than 15%, preferably 10% of the total number of T atoms contained in the zeolite, that is, the sum of the number of T atoms at the outside of the lattice and the number of T atoms in the skeleton.