The invention relates to isomerising light gasoline fractions for producing a high-octane gasoline component and can be used in the oil-refining and petrochemical industries. The isomerisation of light gasoline fractions is carried out at a temperature ranging from 100 to 220 DEG C, a pressure of 1.0-3.5 MPa and a molar ratio between hydrogen and raw material equal to (0.3-10):1 on a catalyst which contains: 0.1-0.8 mass% metals of group 8, 4.0-15.0 mass% sulphuric-acid ion and up to 100 mass% metal oxide composition. Platinum and/or palladium and/or iridium and/or rhodium and/or ruthenium are used in the for of a metal of group 8, and the composition of metal oxides is represented as xFe2O3.MnO2zTiO2Al2O3mZrO2 at the following molar value of coefficients: x=(0.06-3.6)10<-3>, y=(0.11-2.3)10<-3>, z=(0.12-2.5)10<-3>, n=(7.8-21.5)10<-2 >and m=(63.3-74.7)10<-2>, wherein the mass ratio between the sulphuric-acid ion and the composition of metal oxides ranges from 0.042 to 0.178. Said invention makes it possible to increase the isomerisation process stability.