In order to satisfy the requirements of high-precision surface figure error quality and geometry parameters controlling in the on-axis three mirror space camera of large-aperture convex aspheric, multiply process combination and test technique based on the foundation of deterministic lapping and polishing were proposed. In the process stage, ultrasonic milling was firstly introduced to form the aspherical surface form, then robot lapping and polishing were used to rapidly grind and polish, at last, ion beam figuring was used to finish the aspheric fabrication. In the test stage, the geometry parameters and surface figure error of aspheric were firstly controlled by using the coordinate measuring machine(CMM) and then tested by using Hindle sphere testing after the aspheric surface accuracy in interferometric test range. An example for fabricating and testing a convex hyperbolic secondary mirror with diameter of 520 mm was given, the surface figure error of mirror was 0.015λ(λ=632.8 nm), the geometry parameters control accuracy of ΔR and ΔK are 0.1 mm and 0.1%, respectively, all the fabrication results of aspheric satisfy the specifications requirements of the optical design.