A novel design method to achieve beam reconfigurable holographic artificial impedance surface (HAIS) is proposed in this article. Modified modulation equations are presented to achieve the desired single main beam radiation, whereas mushroom-shaped high-impedance surface is introduced to suppress the side lobes. Furthermore, a method called matrix approximation is proposed for the first time, and based on this, reconfigurable radiation beams are implemented. For demonstration purposes, a prototype HAIS is designed at THz band. The demonstrator has a size of approximately 4.7λ × 3.5λ, where λ is the wavelength in free space at 1 THz. Results indicate that along the desired elevation angles, reconfigurable radiation beams at −70°, −60°, −40°, 0°, 40°, 60°, and 70° can be achieved, where all radiations are single main beams. Compared to the conventional metasurface and pattern reconfigurable antenna arrays, the proposed HAIS characterizes low profile and high gain, while avoiding complex feeding networks. All discussions are numerically evaluated and validated by a beam reconfigurable HAIS.