With the gradual development of micro-satellite technology and the extension of application field of earth observation technology, researchers show more concern and attention on how to obtain high-resolution images with microsatellite platform equipped with space telescope. Such microsatellites require the space telescopes with small volume, low mass, and low cost. Deployable telescope is a good choice to meet these requirements, and it has the same capabilities as the traditional space telescope. We investigate a space telescope with smart self-deployable structure. The telescope is folded before launch, the distance between primary mirror and secondary mirror becomes short and the volume of the telescope becomes small, and the telescope extends to its working configuration after it is in orbit. The deployable structure is one of the key techniques of deployable space telescope, and this paper focuses on the design of a self-deployable structure of the secondary mirror. There are mainly three parts in this paper. Firstly, the optics of the telescope is presented, and a Ritchey-Chretien (RC) type optical system is designed. Secondly, the self-deployable structure is designed and the finite element method (FEM) is used to analyze dynamics of the extended telescope. Thirdly, an adjusting mechanism with six degrees of freedom to correct the misalignment of the secondary mirror is investigated, and the kinematics is discussed.