Generalized absolute value equations play an important role in fields such as Economics and Engineering, and solving it has become one of the important problems in computational mathematics and optimization. Based on their equivalent forms and preconditioning techniques, we have conducted research on efficient algorithms for solving generalized absolute value equations, a local preconditioned SOR-like method is proposed. The convergence of this method is discussed. Numerical examples are also given to demonstrate that it outperforms some existing methods in some cases.