Most current strategies for designing tunable locally resonant metamaterials are based on tuning the stiffness of the resonator; however, this approach presents a major shortcoming as the effective mass density is constant at a high frequency. Here, this paper reports a type of tunable locally elastic metamaterial—called “tunable fluid-solid composite.” The proposed metamaterial consists of several liquid or gas inclusions in a solid matrix, controlled through a pair of embedded pumps. Both the band gap and effective mass density at the high frequency can be tuned by controlling the liquid distribution in the unit cell, as demonstrated through a combination of theoretical analysis, numerical simulation, and experimental testing. Finally, we show that the tunable fluid-solid metamaterial can be utilized to manipulate wave propagation over a broad frequency range, providing avenues for vibration isolation and wave guiding.