The flow-induced vibration for an annular leakage-flow system is studied theoretically and experimentally. The annular leakage-flow system consists of a fixed duct, a flexibly mounted inner cylinder allowed to move translationally and rotationally inside the duct, and a viscous fluid flow in the annular passage between the duct and the inner cylinder. A numerical method is developed to analyze the flutter instability of the flow-induced vibration of the inner cylinder. In the method, a critical flow rate is introduced to describe the flutter instability. The experiment on the annular leakage-flow-induced vibration is carried out, and a critical flow rate of the flutter instability is obtained for some annular leakage-flow systems with different passage increment ratios as well as the eccentricities. The calculated results are in good agreement with the experimental results.