Wavefront sensing and control algorithms play a very important role in high-resolution imaging of segmented space telescope. In this paper, a coaxial three-mirror anastigmat system is modeled by Zemax and the primary mirror is a segmented design. After space telescope deployment, the wavefront errors have a wide dynamic range in amplitude and spatial frequency, so a multistage wavefront correction control strategy is proposed to reduce wavefront errors gradually. The wavefront correction process and the wavefront sensing and correction algorithms performed in each step are given in detail. Integrated simulation software is developed to verify our algorithms. Wavefront correction results of segmented primary mirror give a good demonstration of the feasibility of our algorithms.