<p>Adaptive Kriging (AK) model is an important technique for reliability analysis on complex structural systems, but it often encounters an obvious modeling burden when a large training sample pool exists. This paper proposes a novel optimization-based AK method for structural reliability analysis, which takes advantage of the generality and simplicity of Monte Carlo simulation, and uses the gradient descent (GD) algorithm and U learning function to determine the most helpful training samples for reliability analysis of the Kriging model. Based on the analytical property of Kriging model, the gradient of U learning function is analytically derived in the paper. Then, the GD algorithm is enhanced to improve efficiency and avoid obtaining too many unimportant training samples with very low probability density. To overcome the local optimization of the GD algorithm, an AK–GD algorithm based on multiple infill samples is developed to construct the Kriging model, which helps search the training samples with the smallest value of U on a global scale. Finally, four examples demonstrate that the proposed AK–GD method can effectively circumvent the expensive computational burden of Kriging modeling and prediction with a large sample pool, and has significant advantages in providing accurate and stable reliability analysis results.</p>