We design a four-band narrow-band near-perfect absorber based on bulk Dirac semimetal (BDS) metamaterial in the terahertz region. The absorber has a top-to-bottom three-layer structure of a BDS layer, an insulating dielectric slab, and a gold layer. The BDS is flexible and tunable, allowing the Fermi energy level to be adjusted by changing the applied bias voltage, thus changing the absorption characteristics of the absorber. We use the time-domain finite-difference method to simulate the absorption characteristics of the absorber, which could achieve four discrete near-perfect absorption peaks at 0.98 THz, 1.70 THz, 2.02 THz, and 2.36 THz. The absorber is polarization sensitive, and the conversion between four-band absorption and three-band absorption is achieved by changing the incident polarization angle. We also change the structure of the absorber to study the absorption characteristics and break the structural symmetry to achieve a larger number of absorption peaks. Besides, the sensing performance of four-band narrow-band absorption is analyzed, and the maximum sensitivity of the absorber is 112.78 GHz/RIU. The device should have vast application prospects for bio-detection and high-sensitivity biosensing detection.