The application field of space deployable antennas covers mobile communication, navigation, deep space exploration, etc. The traditional space deployable antenna mechanism deploys in a fixed way and mostly in a circular direction in order to expand the space deployable antenna configuration; this paper summarizes the bionic principle that can be used for antenna structure design by studying the tail feather deploying behavior of birds such as peacocks and proposes a new parabolic antenna configuration that imitates the tail feather deploying of birds. The kinematic model of the deployable mechanism is established, and kinematic analysis of the deployable process is carried out on the key rods. The simulation of the rod motion is carried out using ADAMS 2020 software, and the angle change results obtained from the simulation are compared with MATLAB 2020b to verify the correctness of the kinematic equations. The deployment trajectories of the innermost and outermost rib endpoints are analyzed, and the spatial arrangement of the antenna is determined to be in the range of 4 m × 3.5 m. This is a solid foundation for the development of spatially deployable antennas.