Space-deployable mechanisms can be used as supporting structures for large-diameter antennas in space engineering. This study proposes a novel method for constructing the surface design of space reflector antennas based on polar scissor units. The concurrency and deployability equations of the space scissor unit with definite surface constraints are derived using the rod and vector methods. Constraint equations of the spatial transformation for space n-edge polar scissor units are summarized. A new closed-loop deployable structure, called the polar scissor deploy-able antenna (PSDA), is designed by combining planar polar scissor units with spatial polar scissor units. The over-constrained problem is solved by releasing the curve constraint that locates at the end-point of the planar scissor mechanism. Kinematics simulation and error analysis are performed. The results show that the PSDA can effectively fit the paraboloid of revolution. Finally, deployment experiments verify the validity and feasibility of the proposed design method, which provides a new idea for the construction of large space-reflector antennas.