Based on Thomson scattering theory and computer numerical simulation, the influence of circularly polarized laser pulse intensity variation on electron radiation energy spectrum, radiation characteristics in peak radiation direction and space spectrum is studied in this paper. The results show that the spectrum of both backward radiation and peak radiation is shifted and broadened, and this phenomenon becomes more significant with the increase of laser intensity. There is only fundamental wave in the backward radiation spectrum. With the increase of laser intensity, the peak amplitude decreases, and the radiation value is gradually continuous. The peak radiation will produce high order harmonics. The peak amplitude is positively correlated with the laser intensity. As the frequency shift increases, the spectrum overlaps. What′s more, the frequency shift results in continuous spectrum under the action of super strong laser. We further discuss the electron radiation characteristics in the direction of the peak radiation power. We find that the pulse width of the radiation power and the polar angle of the maximum radiation direction have similar characteristics with the change of laser intensity, and both jump at some same special laser intensity. The spatial distribution of electron radiation power is symmetrical in the direction of propagation, and this symmetry is broken when the laser intensity is too large. The results of this study provide an opportunity for further research on the influence of circularly polarized laser on electron radiation characteristics.