High-resolution telescopic imaging is of great importance in astronomy. Compared to the complexity and huge cost of constructing extremely-large telescopes, super-resolution technique which breaks the diffraction limit of the imaging system can enhance the spatial resolution with compact setup and low cost. In this paper, a novel super-resolution telescopic imaging method based on aperture modulation and intensity extrapolation is demonstrated, with both simulated and experimental studies performed. The simulation results show that the method can enhance the resolving power of a diffraction-limited telescopic imaging system by >5 times in noise-free case, and the improvement still reaches ~1.8 times with a signal-to-noise ratio of only ~10. The preliminary experimental results show a resolution enhancement of ~1.36 times for the limitations of the experimental setup. Better performance is possible with the images for reconstruction denoised and registered more precisely. The method is also useful in wide-field microscopy.