The computational efficiency of the reliability-based design optimization(RBDO) can be a critical issue when high-fidelity simulation methods are used. An efficient RBDO framework is presented that utilizes a single-loop RBDO algorithm in which reliability analysis and optimization are conducted in a sequential manner by approximating the limit-state function. A further improvement in computational efficiency is achieved by applying the fixed sensitivity of the limit-state function to the reliability analysis and the equivalent deterministic constraint calculation. To guarantee the convergence of the single loop and the fixed sensitivity algorithm, a trust regionsequential quadratic programming RBDO strategy, is developed. The proposed framework validates low-fidelity approximation models in the trust region radius. The framework is examined by solving an analytical test problem to show that the proposed strategy has the computational efficiency over existing methods while maintaining accuracy. The proposed strategy is applied to a three-dimensional aerodynamic wing design problem to get improved results satisfying probabilistic constraints.