Based on Huygens-Fresnel diffraction integral, an expression describing the focused field of Gaussian beams focused by a lens with spherical aberration is derived. The numerical results show that when the coefficient of the spherical aberration is negative, one can get subdiffraction-limited focusing, that is, one can achieve a smaller focused beam radius than that of no spherical aberration (SA) cases. The larger the coefficient of negative SA, the smaller the focused beam radius. On the contrary, when a Gaussian beam is focused by lenses with positive SA, the focused beam radius is larger than that of no-SA cases. And, the larger coefficient of positive SA, the larger the focused beam radius. The effect of the SA coefficient on the positions where the axial focused intensity is maximum (best focal point) is also discussed.