In modern space optical technology, the requirements for telescope systems have been improved and the systems should have diffraction-limited performance and high resolution. As the aperture diameter is increased, some new technologies need to be applied to correct the large aberrations, reduce the weight of the composites and then to minimize the construction and launch costs. The holographic technique for correcting large aberrations of an inferior quality telescope primary mirror is an attractive approach for this purpose and has been investigated in these years. In this paper, the theory of this method is described and some applications are discussed. A holographically corrected telescope system is designed for further experiments. With this system, the performance of the telescope is prospected to near diffraction-limited. And this kind of holographic optical elements (HOEs) acting as holographic correctors should be useful for making low cost, inferior quality primary mirrors as high quality ones in telescopes.