An adjustable slab-aberration compensator (ASAC) with the ability to compensate the large magnitude inherent wavefront aberrations in the slab width direction is proposed and experimentally demonstrated. The ASAC has a size of 130mm×45mm (effective aperture of 75mm×28mm) and 11 actuators along the length with a contact spacing of 8 mm. The design is optimized by simulations in terms of the mirror’s coupling coefficient with the contact areas, mechanical properties of the driving units, and the mirror thickness. The initial surface figure of the ASAC has PV and RMS values of 55 nm and 10 nm, and the dynamic range is 30 µm. In our experiments, a 20 kW Nd: YAG quasi-continuous wave (QCW) slab laser is further compensated by the ASAC system. The beam quality increases from 15× to 3.5× diffraction limit at 20 kW output after correction. Besides, the proposed ASAC can maintain the surface shape after power shutdown and have good thermal stability. The temperature rise of the ASAC is less than 7 °C in the 20 kW laser correction experiment.