Provided are a catalyst which inhibits light paraffins form being produced in catalytic cracking of heavy hydrocarbons and which effectively produces olefins and a process in which the above catalyst is used to produce olefins from heavy hydrocarbons at a high yield. The catalyst is a catalytic cracking catalyst for catalytically cracking a hydrocarbon raw material, comprising (A) pentasil type zeolite modified with a rare earth element and zirconium and (B) faujasite type zeolite, and the process is a production process for olefin and a fuel oil, comprising bringing a heavy oil containing 50 mass % or more of a hydrocarbon fraction having a boiling point of 180.degree. C. or higher into contact with the catalyst described above to crack it.