Numerical and simulation methods such as FORM, SORM, and MCS are widely used in reliability analysis but face significant challenges in high-dimensional nonlinear problems due to limitations in both efficiency and accuracy. Surrogate modeling, such as Kriging, can help mitigate these challenges, but it requires integration with analytical methods for optimal performance. This paper proposes an efficient approximate integral method based on the Kriging surrogate model (KAIM), which integrates the Kriging Surrogate Model with an optimized approximate integration technique to specifically addressing extreme nonlinearity and dimensionality challenges. By analyzing the geometric properties at the limit-state surface, KAIM develops an optimized integral method that better captures nonlinear behavior compared to traditional quadratic approximations. The method further decomposes the analysis space into spherical elements and uses Kriging-predicted errors to dynamically refine the integration process, improving computational efficiency and result reliability. Numerical examples demonstrate that KAIM significantly outperforms traditional methods in nonlinear contexts, achieving higher accuracy in failure probability estimation while reducing computational costs.