Phase-sensitive optical time-domain reflectometry (Φ-OTDR) has been proposed for distributed vibration sensing purpose over recent years. Emerging applications, including seismic and hydroacoustic wave detection, demand accurate low-frequency vibration reconstruction capability. We propose to use the direct-detection Φ-OTDR configuration to achieve quantitative demodulation of external low-frequency vibrations by phase-shifted dual-pulse probes. Simultaneous pulsing and phase shifting modulation is realized with a single acousto-optic modulator to generate such probes, relaxing the need for an additional optical phase modulator. In the experiments, vibrations with frequency as low as 0.5 Hz are successfully reconstructed with 10 m spatial resolution and 35 dB signal-to-noise ratio. Excellent linearity and repeatability are demonstrated between the optical phase demodulation results and the applied vibration amplitudes. The proposed method is capable of quantitative demodulation of low-frequency vibrations with a cost-effective system configuration and high computation efficiency, showing potential for commercial applications of distributed seismic or hydroacoustic wave acquisition.