Classical designs of acoustic meta-absorber usually have a trade-off between bandwidth, efficiency and thickness. Here, we introduce the concept of nonlocal acoustic metasurface absorber by using a bridge structure connecting resonating unit cells to improve the performances of the meta-absorber. By utilizing the coupling effect between the adjacent unit cells, ultra-broadband sound absorption is achieved with deep-wavelength thickness. The physical mechanism of the nonlocal acoustic metasurface absorber is investigated by developing analytical models. We theoretically and numerically study the nonlocal metasurface with connecting bridge and the traditional metasurface without bridge. The nonlocality can introduce three specific effects: 1. Optimizing of effective acoustic impedances. 2. Shift of FabryPerot resonant frequencies. 3. Strengthening of the coupling effects between adjacent unit cells. These effects help to improve the bandwidth and the efficiency of the acoustic meta-absorber. We numerically and experimentally achieve an averaged absorption coefficient larger than 0.9 within the ultra-broadband bandwidth from about 600 Hz to 2600 Hz, with a sample thickness of 6.8 cm, , /9 for the lowest frequency. Our finding demonstrates the advantage of non-local acoustic metasurface to conceive subwavelength sound meta-absorber.