As a common aberration, spherical aberration has great influence on beam propagation in optical systems. In order to study the influence on beams in the spherically aberrated fractional Fourier transform system, based on the Collins formula, the light field distribution expressions of the cosine-Gaussian beams through spherically aberrated and non-spherically aberrated fractional Fourier transform system are derived. With the example of Lohmann Ⅰ, the output transverse intensity distribution in spherically aberrated fractional Fourier transform system, non-spherically aberrated fractional Fourier transform system, the relationship between the intensity distribution on axis and the coefficient of spherical aberration in different transform orders or different modulation parameters are studied through numerical calculation. It is shown that the spherical aberration of lens has great influence on the output transverse intensity distribution, and whether the spherical aberration is positive or negative also reswits in notably different effects. The effect on the on-axis light intensity caused by the spherical aberration of lenses is different for different transform orders and modulation parameters.