Based on the generalized Huygens-Fresnel diffraction integral formula, field distribution expressions of Bessel beams passing through a spherical aberration fractional Fourier transform system with an aperture are derived when we take Lohmann Ⅰ type optical system as an example. Propagation characteristics of Bessel beams in ideal fractional Fourier transform system and the influence rule of aperture and spherical aberration on beam propagation are calculated by numerical simulation. The results show that Bessel beams do not maintain propagation invariability after passing through a fractional Fourier transform system. When the system only contains an aperture, a hollow beam can be obtained at the conventional Fourier transform plane. When the system contains aperture and spherical aberration, beams with good focusing property and high central light intensity can be obtained with positive spherical aberration. Light intensity distribution on the axis is mainly affected by the aperture when the aperture size is small, and it is influenced by spherical aberration when the aperture size exceeds a critical value.