PURPOSE: To obtain a catalyst for the selective hydrogenation of a feedstock including diolefinic and/or acetylenic unsaturated compounds by carrying a group VIII metal and Ga or In on a catalyst support.

CONSTITUTION: At least one group VII metal (e.g. Pd) and at least one group IIIA metal selected from Ga and In are carried on a catalyst support (e.g. silica). A solution of a compound of the group IIIA metal having such a concentration of the metal as to fix 0.01-10 wt.% metal is impregnated into the support, a solution of a compound of the group VIII metal having such a concentration of the metal as to fix 0.01-10 wt.% metal is then impregnated and firing is carried out at 110-600°C to produce the objective catalyst for the conversion of hydrocarbons. When this catalyst is used, a feedstock including diolefinic and/or acetylenic unsaturated compounds is selectively hydrogenated.