By using the two technologies of frequency division multiplexing and in-phase/quadrature (I/Q) receiving, this paper proposes a distributed optical fiber vibration sensing demodulation scheme with high spatial resolution and large bandwidth. Theoretical analysis and numerical simulation are carried out. This distributed vibration sensing structure is composed of a Mach-Zehnder interferometer (MZI) and a time-gated digital optical frequency-domain reflectometry (TGD-OFDR). Specifically, the phase of the MZI output signal is demodulated by the homodyne method to detect the frequency and amplitude of the vibration signal, whereas TGD-OFDR enables the positioning of the vibration signal through heterodyne detection. The numerical simulation results show that the upper limit of the vibration frequency which the proposed system can detect reaches the order of magnitude of MHz, and the spatial resolution on the 4-km sensing optical fiber is up to 0.5 m. This distributed vibration sensing system, with the advantages of high spatial resolution and large detection bandwidth, has application potential in civil infrastructure health monitoring and oil and gas pipeline leakage monitoring.