In this paper, two new iterative methods for solving generalized absolute value equations (GAVEs) are proposed and investigated using the single-step iteration (SSI) approach. The proposed iterative methods are Picard-SSI and nonlinear SSI-like methods. In the implementation of the Picard-SSI method, we have used the SSI method as an inner solver. The convergence of the proposed method for solving GAVE is analyzed under reasonable constraints. Several numerical examples are given to illustrate the efficiency and implementation of the proposed methods.