Maleic anhydride is prepared by the catalytic oxidation of unsaturated hydrocarbons having 4 to 6 carbon atoms, at a temperature of from 350.degree. to 500.degree. C., in the presence of a catalyst which is produced by a method wherein a mixture of a titanium oxide and a vanadium compound in an atomic ratio of from 1 to 15 is calcined at a temperature of from 630.degree. to 1000.degree. C. to prepare a precursory catalyst, and wherein a gas mixture containing an organic phosphorus compound and a carrier gas is brought into contact with a mass of the percursory catalyst at a supply rate of the phosphorus compound being from 0.01 to 10 millimoles/hr per 1 ml of the mass of the percursory catalyst and at a temperature of from 350.degree. to 600.degree. C. during when a total amount of from 0.3 to 30 millimoles of the phosphorus compound per 1 ml of the mass of the precursory catalyst passes through the mass of the precursory catalyst.