In order to achieve sub-diffraction limited imaging of the distant objects with telescope under the dynamical disturbance of the atmospheric turbulence, the optical super-oscillation phenomenon was utilized to locally compress the point spread function of the telescope. Theoretical study was performed to investigate the imaging resolution improvement with super-oscillation phenomenon. In the case of the modest atmospheric turbulence, the adaptive optics closed-loop root mean square of the simulated residual wave front error is about 1/15 of wavelength. The numerical full width at half maxima of the super-oscillation spot is about 0.75 times of the Airy spot at the working wavelength of 632.8 nm. In addition, the imaging results of the two holes with different center-to-center distances validate that the resolving ability of the super-oscillation telescope is about 0.80 times of the Rayleigh criterion. Different root mean square of the residual wave front error would result in the diffractive compression ratio of the telescope’s point spread function and the improvement of the imaging resolution. It is believed that this study provides a practical method for the high-precision star positioning and the super-resolution telescope etc.