The spherical aberration is an important factor affecting the resolution power of super-oscillatory telescopic systems. The reason is that the spherical aberration leads to a high sidelobe in the field of view of the intensity point spread function, which reduces the resolution of the system. In this paper, the effect of the spherical aberration on imaging in a super-oscillatory telescopic system is analyzed and the allowable range of the primary spherical aberration is determined. Based on the principle of optical super-oscillatory and the optimization method of linear programming, a super-oscillatory telescopic system is designed. A resolution of 0.68 times the Rayleigh criterion can be achieved under a working wavelength of 532 nm. A mathematical model for quantitative analysis of the super-oscillatory telescopic system with the spherical aberration is established. The system can distinguish the three-slit target under the interference of the primary spherical aberration with a root mean square (RMS) no more than 0.041 times wavelength. The imaging effect of the narrow band working wavelength in the spherical aberration system is analyzed. This paper has potential applications in optical measurement, environmental monitoring, super-resolution telescope, and other fields.