We investigate the propagation behavior of the low-frequency topological interface state of the flexural wave in the locally resonant metastructure and analyze the tunability of the sub-wavelength interface states by the piezoelectric shunting circuit. One homogeneous thin beam is periodically attached with local resonant beams, which connect shunted piezoelectric actuators. The folding band obtained by merging two primitive unit cells into one new element can generate a Dirac point below the low-frequency locally resonant bandgap. This folding point is opened to develop one new bandgap originated from the Bragg scattering effect by breaking the mirror symmetry. Then, topological transitions are demonstrated during the distance variation between two adjacent resonances. The interface state’s existence is further confirmed by using steady and transient analysis of the heterostructure, composed of two media with different topological properties. Finally, we show the relationship between the interface frequency and the capacitance ratio and research the influence of the distance parameter on the topological interface state. Because of the tunability of elastic waves by the piezoelectric shunting circuit, our design has potential for applications such as energy harvesters, filters, and physical switches.