The invention provides a preparation method of a catalyst containing a Y-type molecular sieve, the catalyst is obtained by mixing, kneading, extruding and rolling mixed slurry of the Y-type molecular sieve, alumina sol, pseudo-boehmite, silica sol, clay, acid and water, the Y-type molecular sieve is an NH4Y molecular sieve prepared by carrying out ammonium exchange treatment on a NaY molecular sieve, and the NH4Y molecular sieve is a Y-type molecular sieve prepared by carrying out ammonium exchange treatment on the NH4Y molecular sieve. And contacting the obtained NH4Y molecular sieve with a salt solution containing alkali metal ions and/or a salt solution containing alkaline earth metal ions, filtering, washing, drying, carrying out hydrothermal aging on the obtained product, contacting with an acid solution, and recovering the product, wherein the alkali metal is selected from rubidium and cesium, and the alkaline earth metal is selected from strontium and barium.