An integrated aberration-compensating module (IACM), consisting mainly of an adjustable slab-aberration compensator, a one-dimensional Shack-Hartmann wavefront sensor, and a data processor, which meet the urgent requirements of correcting the specific wavefront aberrations of a slab laser based on an off-axis stable-unstable resonator, is designed and experimentally demonstrated. Benefits include compactness, robustness, simplicity, automation, and cost-effectiveness. The particular wavefront aberrations of the 9 kW level quasi-continuous-wave Nd:YAG slab laser, which have characteristics of asymmetry, large amplitude and gradient, high spatial frequency, and low temporal frequency, were measured and theoretically analyzed. In the experiment, the wavefront aberrations of the slab laser were corrected by the IACM. At the average output power of 9 kW, the diffraction-limited factor β was improved from 20.3 times diffraction limit (DL) to 3.6 times DL. The peak-to-valley and root-mean-square values of aberrations were reduced from 9.6 to 0.85 µm and from 2.86 to 0.18 µm within five iterations of the IACM, respectively. Moreover, The IACM is capable of maintaining the compensating surface figure after power-off.