© 2023 Walter de Gruyter GmbH, Berlin/Boston 2023.In this study, we concentrate on solving the problem of non-Lipschitz absolute value equations (NAVE). A new Bezier curve based smoothing technique is introduced and a new Levenberg-Marquardt type algorithm is developed depending on the smoothing technique. The numerical performance of the algorithm is analysed by considering some well-known and randomly generated test problems. Finally, the comparison with other methods is illustrated to demonstrate the efficiency of the proposed algorithm.