We propose a holographic adaptive optics system based on holographic wavefront sensor and 21-element deformable mirror, and analyze the wavefront correction ability of the system in this paper. The principle of holographic wavefront sensor is described, and its numerical model is provided by fast Fourier transform algorithm in the thin hologram approximation. Then, the wavefront correction ability of 21-element deformable mirror is analyzed with its numerical model. Finally, the aberration compensation of the system is simulated and an experimental device is set up to verify the feasibility of the proposed adaptive optics system.