Aero-engine turbine components have complex structures, harsh service load environments, and strong nonlinear structural responses, so it is difficult to establish the explicit limit state function, which is a typical nonlinear implicit function reliability analysis problem. To address this challenge, based on Particle Swarm Optimization and a Back Propagation Neural Network (PSO-BPNN), a reliability analysis approach is proposed in this paper. In the proposed method, the PSO algorithm is employed to optimize the initial weights and biases of the BPNN. This global optimization capability prevents the neural network from falling into local extrema and mitigates overfitting, thus improving the accuracy and generalization of the BPNN in approximating implicit limit state functions. On this basis, the Monte Carlo simulation (MCS) method is used to call the established neural network to calculate the failure probability, and the original implicit limit state function is not needed at this time. The proposed PSO-BPNN approach exhibits higher computational precision and efficiency, particularly for problems with strong nonlinearity and high dimensionality. Numerical examples are used to verify the efficiency and accuracy of the proposed approach, which is further applied to analyze the reliability of an aero-engine turbine casing structure. The results demonstrate that the proposed method not only offers high computational efficiency and accuracy but also provides significant advantages in handling complex nonlinear implicit reliability analysis problems. This indicates its strong potential to serve as a reliable and practical tool for engineering reliability analysis, particularly in the aerospace domain, where structural components often operate under extreme conditions.