Nonlinear absorption coefficient and modulation depth stand as pivotal properties of nonlinear optical (NLO) materials, while the existing NLO materials exhibit limitations such as low nonlinear absorption coefficients and/or small modulation depths, thereby severely impeding their practical application. Here we unveil that introducing Jahn-Teller distortion in a Mott-Hubbard system, (MA)2CuX4 (MA = methylammonium; X = Cl, Br) affords the simultaneous attainment of a giant nonlinear absorption coefficient and substantial modulation depth. The optimized compound, (MA)2CuCl4, demonstrates a nonlinear absorption coefficient of (1.5 ± 0.08) × 105 cm GW-1, a modulation depth of 60%, and a relatively low optical limiting threshold of 1.22 × 10-5 J cm-2. These outstanding attributes surpass those of most reported NLO materials. Our investigation reveals that a more pronounced distortion of the [CuX6]4- octahedron emerges as a crucial factor in augmenting optical nonlinearity. Mechanism study involving structural and spectral characterization along with theoretical calculations indicates a correlation between the compelling performance and the Mott-Hubbard band structure of the materials, coupled with the Jahn-Teller distortion-induced d-d transition. This study not only introduces a promising category of high-performance NLO materials but also provides novel insights into enhancing the performance of such materials.