With the increasing scarcity of spectrum resources, terahertz wave technologies have attracted more and more attention in recent decades, and have made tremendous progress. Terahertz wave referring to electromagnetic waves with a frequency in a range of 0.1－10 THz has a wide range of applications in wireless communication, nondestructive imaging and remote sensing. Due to the advantages of high absorption, ultra-thin thickness, frequency selectivity and design flexibility, metamaterial absorbers have attracted more attention in terahertz band. In this paper, two terahertz metamaterial absorbers with different performances are designed which are named “T” terahertz multi-band absorber and “T” terahertz tunable broadband absorber, respectively. The absorbers are both comprised of three layers: metal substrate, matched dielectric layer and surface metamaterial layer. The main structures of these two absorbers are composed of four T-shape Au plates on the top of polyimide dielectric layer and an Au sheet acting as a bottom layer. The only difference between these two absorbers is that the terahertz broadband tunable absorber possesses a square photosensitive silicon in the metamaterial layer. The simulations results show that the terahertz multi-band absorber has six absorption peaks at 2.918, 3.7925, 4.986, 6.966, 7.2685, and 7.4665 THz, with the absorptivity peaks of 95.631%, 99.508%, 96.34%, 94.835%, 96.485%, 94.732%, respectively, and the average absorption rate is 96.26%. Terahertz tunable broadband absorber has the characteristics of broadband absorption. When the conductivity of silicon is 1600 S/m, the absorber reaches its absorption peak at 0.786 THz with the absorptivity of 99.998%, and the frequency bandwidth with the absorption rate exceeding 90% reaches 240 GHz. The more interesting thing is that by changing the conductivity of silicon, the terahertz tunable broadband absorber shows the ability to dynamically control the existence of absorption band and adjust the frequency position of absorption peak. For terahertz tunable broadband absorber, the frequency of absorption peak can be regulated in a bandwidth of about 30 GHz. The terahertz wave absorbers designed in this paper possess rather simple structures, therefore the proposed absorbers are easy to fabricate. Because of these excellent properties, the absorbers may have potential applications in optical switch, optical detection, optical imaging, band-stop devices, and other fields.