Abstract Topological acoustic insulators demonstrate unusual characteristics in manipulating sound wave, which attract much attention from researchers. However, most of the recent researches are based on passive system, hampering their dispersion tunability. In this paper, a broadband subwavelength tunable fluid filling acoustic topological metastructure is studied. It is composed of perforated cells with tunable water height in the hole, which enables the dispersion of the edge state to be tuned. The inversion symmetry is broken by expanding and shrinking the adjacent holes in the unit cell. Thus, the valley Hall states with opposite Chern number form at the K point in the Brillouin zone. The edge states emerge at the boundary of the different valley Hall phases. The robustness of the edge states is verified by the straight and Z-shaped waveguide. Furthermore, the dispersion of the edge state can be altered continuously by raising and reducing the water height, giving rise to broadband variable topological states, which greatly expands the bandwidth from 40 Hz to 1033 Hz. This work offers a new method to control the topological states and shows great potential for practical application.