The invention discloses an experiment device for measuring a low-frequency elastic wave response characteristic after liquid annular air cut and a corresponding experiment method. The experiment device comprises a mineshaft annular air simulation part, a liquid circulation control part, a bubble generation and circulation control part and an elastic wave response characteristic measurement part. According to the experiment device for measuring the low-frequency elastic wave response characteristic after liquid annular air cut, under the condition of annular liquid quiescence or flow, conditions of the pressure, the bubble size and the gas volume fraction are controlled, particularly stable control can be achieved in the range of low gas volume fraction (0.5-2%), the phase velocity and the reduction of an elastic wave after the annular air cut are measured, the structure is simple, the reliability of the measurement data is high, and the experiment cost is low.