An optically tunable terahertz metamaterial absorber with multiple absorption bands is designed. The CST 2014 simulation software is used to simulate the structure of the designed metamaterial absorber. We designed four metallic bars with varied lengths on the substrate to realize that the perfect absorption of the designed metamaterial absorber which can be controlled from single-band to dual-band. The electric field distributions at four absorption peaks of the metamaterial absorber is simulated to further study the transmission characteristics of the metamaterial absorber. The photosensitive medium in the gap of two metallic bars is further irradiated by a pump laser to realize the optically-controlled tuning of the absorber. The simulation results show that the absorptivity of the designed metamaterial absorber at four absorption peaks all exceed 95%. The resonance mechanism of the designed structure is attributed to the overlapping of four resonance frequencies corresponding to the four metallic bars with different lengths. Hence, the perfect absorber can be dynamically controlled from four-band to dual-band.