Abstract: The HL-RF algorithm is widely used for first order second moment reliability method (FOSM) due to its simplicity and efficiency. It shows high efficiency for mildly nonlinear performance functions. However, it will lead to oscillation, bifurcation, periodic solution, and even non-convergence when the performance function is highly nonlinear. Thus, this paper proposes a modified chaos control method, based on chaos control theory, to overcome this drawback. The modified chaos control method improves the efficiency of the chaos control method. A function type criterion is further introduced to identify the performance function type. If the iterative point converges to the most probable failure point gradually, the HL-RF algorithm is adopted; otherwise, the modified chaos control method is selected during the iterative process. The numerical examples show that the proposed method is efficient for oscillating problems. In comparison with HL-RF algorithm, the modified chaos control method is more robust and efficient.