The first-order correction to the field of ultra-short circularly polarized laser was studied. This theory was used to study the dynamics characteristics of incident electron in the circularly polarized intense laser pulse field, and the acceleration phenomenon was found. For the pulse duration τ0≤30, where τ0 is normalized by 1/ω and ω is the laser frequency, the paraxial approximation is basically consistent with the first-order correction. But when τ0>30, the paraxial approximation deviates from the first-order correction. The electron bunch acceleration effect was also confirmed by using the first-order correction when τ0=100 and τ0=300. At last, the energy distribution spatial distribution and as to the pulse duration was obtained. It is also found that the amount of acceleration electrons increases and these electrons can gather under τ0=300.