A method for preparation of ethylene and propylene by catalytic cracking using a fluid-bed catalyst. The main technical problems to be solved are a relatively high reaction temperature, and low activities and poor selectivities of the catalyst at a low temperature, during the reaction for preparing ethylene and propylene by catalytically cracking naphtha. The fluid-bed catalyst is a composition of the chemical formula Mo.sub.1.0V.sub.aA.sub.bB.sub.cC.sub.dO.sub.x based on stoichiometric ratio. The method using the fluid-bed catalyst has satisfactorily solved the above-mentioned problems, and is useful in the industrial production of ethylene and propylene by catalytically cracking naphtha.