In this paper, a novel method for approximate analytic series solution called Multi-step Laplace Adomian Decomposition Method (MLADM) has been proposed for solving the chaotic Genesio system (CGS). The proposed method is a modification of the classical Laplace Adomian Decomposition Method (LADM) with multi-step approach. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. Comparison of the results with RK4 confirms that MLADM performs very high accuracy. Results show that MLADM is a very promising method for obtaining approximate solutions to CGS. Moreover, it can be readily employed to solve other chaotic systems.