Distributed optical fiber sensing exploring forward stimulated Brillouin scattering (FSBS) has received wide attention, as it indicates a new sensing method to measure the liquid property surrounding an optical fiber. In the existing techniques, backward stimulated Brillouin scattering is adopted for detection of the sensing signal, which requires time-consuming signal acquisition and post-processing. In this work, an approach that distributedly measures FSBS spectra is proposed and demonstrated based on coherent detection. While an excitation pulse with single-frequency amplitude modulation is used to induce a guided acoustic mode in the fiber, a following pulse is adopted to probe the induced phase modulation. Using a chirped fiber Bragg grating array, an enhanced-backward-propagating sensing signal is generated from the probe pulse. Heterodyne coherent-detection-based phase demodulation is then realized by mixing the sensing signal with a local oscillator. The FSBS spectra can then be reconstructed from the beat signals with only one round of frequency sweeping. With significantly accelerated signal acquisition and simplified post-processing, the proposed distributed acoustic sensing system has achieved spatial resolution of 5 m over a 500-m sensing range.