The novel technical scheme of super cavity is proposed. Using Compton scattering theory, the high brightness laser synchrotron source (LSS) based on the technique of super cavity, including radiation wavelengths, photon yield and radiant power, are calculated and discussed. The effects of the electron beam quality and the laser power loss on the photon yield and radiant power of laser synchrotron source are discussed. The results show that the γ-ray with energy up to 10.975 MeV are expected to be produced by Compton vertical scattering of far-field infrared laser photons on the 3.5 GeV electrons bunches, the photon yield of a single electron are direct proportion to the power and wavelength of laser, and inverse proportion to the sectional area of laser beam. The radiant power of a single electron is direct proportion to the power of laser and square of Lorentz factor, and inverse proportion to the sectional area of laser beam.