Summary: In this paper, a nonlinear conjugate structural first-order reliability method is proposed using three-term conjugate discrete map-based sensitivity analysis to enhance convergence properties as stable results and efficient computational burden of nonlinear reliability problems. The concept of finite-step length strategy is incorporated into this method to enhance the stability of the iterative formula for highly nonlinear limit state function, while three-term conjugate search direction combining with a finite-step size is utilized to enhance the efficiency of the sensitivity vector in the proposed iterative reliability formula. The proposed three-term discrete conjugate search direction is developed based on the sufficient descent condition to provide the stable results, theoretically. The efficiency and robustness of the proposed three-term conjugate formula are investigated through several nonlinear/ complex structural examples and are compared with several modified existing iterative formulas. Comparative results illustrate that the three-term conjugate-based finite step length formula provides superior efficiency and robustness than other studied methods.