A broadband and high-sensitivity ultrasound sensing system based on a low-noise random fiber laser (RFL) with a disordered fiber Bragg grating array (FBGA) feedback is proposed and demonstrated. The disordered FBGA achieves a high-Q value and a large spectral slope, resulting from complex interference among multiple randomly separated FBGs, which contributes to a narrow-linewidth and low-noise RFL sensor with high sensitivity. Experimental results show that the high-Q FBGA-based RFL achieves ultrasound sensing up to 27.9 MHz with an averaged signal-to-noise ratio (SNR) of 33 dB, which is extended by 6.7 MHz and increased by 13 dB than the RFL based on a random fiber grating (RFG) feedback. These improvements are attributed to the suppression of intensity noise by more than 10 dB at high frequencies and the 300 times greater spectral slope of the FBGA-based RFL compared to the RFG-based RFL.