Composite catalysts based on cobalt- or nickel-modified mordenite zeolite (module 17) and sulfated zirconium dioxide have been synthesized. With the participation of these catalysts, the isomerization conversion of gas gasoline at low temperature (160–200 °C) and normal atmospheric pressure was studied. The role of each of the components of the catalyst in this process was studied. It has been found that the addition of a metal (cobalt or nickel) to the zeolite increases the stability of the catalytic system, zirconium dioxide lowers the process temperature, and sulfate anions facilitate isomerization. The components of the catalytic system are not active individually in this process under the given conditions, and these components carry out the process together. It was determined that with the participation of the synthesized catalytic system, the low and high molecular weight components of gas gasoline were converted into medium molecular weight and mainly iso-C5-C6 alkanes. Thus, it was shown that the synthesized catalytic systems have the ability to convert gas gasoline into environmentally friendly, high-octane gasoline components.