Based multi-phase screen numerical simulation, the influences of on-axis scintillation of focus Gaussian beams propagating in the turbulent atmosphere on several typical aberrations are investigated quantitatively. It is found that astigmatism and coma aberrations can restrain and promote the axis-scintillation to some extent, respectively. Stronger coma and astigmatism aberrations can forward and delay the appearance of scintillation saturation, respectively. The distribution of intensity deviates from log-normal distribution when turbulence strength is weaker. It is close to log-normal distribution when the intensity of turbulence rises. The skewness of the intensity distribution is less than zero and its kurtosis is greater than zero basically. Under weak or moderate turbulence intensity, the distribution of intensity fluctuation is always determined by aberrations when the aberration is big enough, however, the effects of turbulence play the main role on the distribution of intensity fluctuation and the aberrations mainly affect the fluctuation distributions of weak intensity areas when the weight of aberration is small. The strong turbulence influences the probability distribution of intensity fluctuation mostly, and the distribution fits to log-normal distribution approximately.