This paper presents a novel shape memory metamaterial, which can achieve adaptively tunable bandgaps for ultra-wide frequency spectrum vibration control. The microstructure is composed of a Shape Memory Alloy (SMA) wire and a metallic spring combined together with bakelite blocks, loaded by a lumped mass made of lead. The adaptive bandgap mechanism is achieved via the large deformation of the metamaterial unit cell structure during the heating and cooling cycle. By applying different heating temperature on the SMA wire, morphing microstructural shapes can be achieved. Parametric design is conducted by adjusting the lead block mass. Finally, an optimized microstructural design rendering a large deformation is chosen. Finite element models (FEMs) are constructed to analyze the dynamic behavior of the metamaterial system. Effective mass density of the unit cell is calculated to investigate and demonstrate the bandgap tuning phenomenon. In the simulation, two extreme shapes are simulated adhering to the experimental observations. The effective negative mass density and the moving trends are obtained, representing the development and shifting of the bandgaps. The width of the bandgap region covers about 50 Hz from the room-temperature state to the heating state. This enables the vibration suppression within this wide frequency region. Subsequently, a metamaterial chain containing ten unit cells is modeled, aligned on an aluminum cantilever beam. An external normal force with a sweeping frequency is applied on the beam near the fixed end. Harmonic analysis is performed to further explore the frequency response of the mechanical system. The modeling results from modal analysis, effective mass density extraction, and harmonic analysis agree well with each other, demonstrating the prowess of the proposed shape memory metamaterial for ultra-wide frequency spectrum control.