In this Letter, we demonstrate a highly sensitive quasi-distributed fiber-optic acoustic sensing system. This system interrogates a weak reflector array by using phase-sensitive optical time domain reflectometry with coherent detection. A phase-noise-compensated configuration is proposed to reduce the influence of 1/f noise, which is the main limitation when coherent detection is used in this high-sensitivity system. In the experiment to simulate the scenario with a link loss of 20 km fiber and 10 m array interval, the noise level shows an acoustic signal sensitivity of 3.84 pϵ/√Hz at 10-2500 Hz.