A novel distributed fiber vibration sensing technique based on phase extraction from time-gated digital optical frequency domain reflectometry (TGD-OFDR) which can achieve quantitative vibration measurement with high spatial resolution and long measurement range is proposed. A 90 degree optical hybrid is used to extract phase information. By increasing frequency sweeping speed, the influence of environmental phase disturbance on TGD-OFDR is mitigated significantly, which makes phase extraction in our new scheme more reliable than that in conventional OFDR-based method, leading to the realization of long distance quantitative vibration measurement. By using the proposed technique, a distributed vibration sensor that has a measurement range of 40 km, a spatial resolution of 3.5 m, a measurable vibration frequency up to 600 Hz, and a minimal measurable vibration acceleration of 0.08g is demonstrated.