In order to satisfy the demand for the space diffraction telescope in space exploration, a new deployable space diffractive telescope was designed, which aimed at one diffraction optical system. Firstly, the structural form and geometrical sizes of the spontaneous deployable structure used in this article were preliminarily designated through the Serrurier truss theory and the optimization design theory, and a new spontaneous deployable structure was designed aiming at one diffractive optical system. Secondly, the finite element model of the deployable structure was built, and its deployment characters were analyzed. Finally, the prototype of the spontaneous deployable structure was built up and the experiment was carried out to study its characteristics. Experimental results indicate that the deployable structure is 2.9 m in length, its repetitive deploy accuracy can reach less than 2 mm, the decentration is less than 0.3 mm. Besides, the deploy accuracy can be adjusted to micrometer level by actuators when it has deployed. It can satisfy the deployment structure′s requirements of simple mechanics, low mass, steady and reliable deployment, as well as higher precision for the space diffractive telescope.