In order to satisfy the demands for diffractive telescopes in space exploration, a new deployable space diffractive telescope is designed. The structure and geometrical sizes of the spontaneously deployable telescope are preliminarily designated through the Serrurier truss principle and the optimized design theory. The finite element model of the deployable structure is established, and its deployed characteristics are analyzed. The prototype of the spontaneously deployable structure is constructed and some experiments are carried out to study its characteristics. Experimental results indicate that the deployable structure is 2.95 m in length, its repetitive deployed precision can reach less than 2 mm, the off-center error is less than 0.3 mm, and its deployed precision can be adjusted to micrometer level by actuators when it has deployed. It has simple structure, low mass, steady and reliable deployment, as well as higher precision for space diffractive telescopes.