A tunable six-band terahertz metamaterial absorber (MMA) was designed and simulated in this work, consisting of a MoS2 or BP monolayer as loss layer, a dielectric substrate and a metal-insulator phase change material VO2. By simultaneously adjusting the thickness and the conductivity of VO2 or the carrier concentration, the absorption spectrum can be dynamically tuned. The numerical simulation results showed that almost every absorption peak at six frequencies was above 90% under TE polarization when the loss layer was set as MoS2 or BP. Furthermore, the absorber with either of these two 2D materials as loss layer was insensitive to incident angles. Additionally, the influence on absorption peaks by regulating the structure parameters of the absorber was also briefly investigated. The proposed absorber, which exhibited superior absorption characteristics with either selected loss layer adopting the same simple physical unit structure, may provide a new direction for the design of tunable terahertz devices.