The invention relates to an air-cooled ozone generator of tubular type which has a tubular outer electrode, a tubular dielectric, for instance of glass, arranged inside the outer electrode, and an inner electrode in the form of a metal coating on the inner side of the dielectric. The outer electrode and the dielectric are spaced apart and the resulting intermediate annular gap forms a discharge space in which oxygen is converted to ozone. The ozone generator is operated by means of a low-voltage, high-frequency AC source connected to the electrodes. The outer electrode has cooling flanges, and inside the inner electrode there is provided at least one heat dissipating metal body insertable in the inner electrode and expandable to abutment against the inner electrode. Preferably, the metal body also serves as an electric connection for connecting the inner electrode to the voltage source. The metal body preferably consists of a sheet formed into a cylinder with two inwardly directed flanges.