A tunable relativistic magnetron with axial radiation operating at 2 mode is investigated by three-dimensional particle-in-cell simulation in this paper. The tuning is realized by filling solid dielectric material into the cavities of the interaction region. The effects of changing the relative permittivity and the inner radius of the dielectric material on the operating frequency, the average output power and the efficiency are analyzed. Then the principle of the tuning is demonstrated. The simulation results show that under the unchanged structure parameters and the work point, the relativistic magnetron realizes the tuning from S band to L band by varying the relative permittivity or the inner radius of the solid dielectric material. Furthermore, with inserting the dielectric material, the output capability of the relativistic magnetron is improved. When the relative permittivity is 615 and the radius is 4.184.40 cm, the increase in efficiency can reach 80%, the decreased frequency range is less than 55%.