The increasing demand for high-performance optical components in optical integrated systems calls for tunable filter with broadband and narrowband tunability. Here, we propose four designs of tunable metasurface absorber (TMA) composed of suspended nanodisk metasurface with single- and dual-layer Al/SiO₂ and Al/LiNbO₃ thin-films on Si substrate coated with an Al mirror layer atop, which are denoted as TMA-S1, TMA-S2, TMA-L1, and TMA-L2, respectively. Four devices show the resonant wavelengths with ultrabroad tuning ranges and perfect absorptions. The broadest tuning ranges are 239 nm, 400 nm, 293 nm, and 400 nm, which can be designed to span 60%, 100%, 73% and 100% of visible spectra range for TMA-S1, TMA-S2, TMA-L1 and TMA-L2, respectively. TMA-S2 and TMA-L2 exhibits the characterizations of stronger absorption intensity and narrower bandwidth compared to TMA-S1 and TMA-L1. Furthermore, the absorption resonances of devices are red-shifted by changing ambient refractive index. The corresponding sensitivities are 292.85 nm/RIU, 277.14 nm/RIU, 458.57 nm/RIU and 401.25 nm/RIU for TMA-S1, TMA-L1, TMA-S2 and TMA-L2 respectively. The proposed designs of TMA open an avenue to the possibilities for high-efficiency wavelength-selective devices and high-performance refractive index sensors in the visible spectral range.