To improve the computational efficiency and accuracy of multi-objective reliability estimation for aerospace engineering structural systems, the Intelligent Vectorial Surrogate Modeling (IVSM) concept is presented by fusing the compact support region, surrogate modeling methods, matrix theory, and Bayesian optimization strategy. In this concept, the compact support region is employed to select effective modeling samples; the surrogate modeling methods are employed to establish a functional relationship between input variables and output responses; the matrix theory is adopted to establish the vector and cell arrays of modeling parameters and synchronously determine multi-objective limit state functions; the Bayesian optimization strategy is utilized to search for the optimal hyperparameters for modeling. Under this concept, the Intelligent Vectorial Neural Network (IVNN) method is proposed based on deep neural network to realize the reliability analysis of multi-objective aerospace engineering structural systems synchronously. The multi-output response function approximation problem and two engineering application cases (i.e., landing gear brake system temperature and aeroengine turbine blisk multi-failures) are used to verify the applicability of IVNN method. The results indicate that the proposed approach holds advantages in modeling properties and simulation performances. The efforts of this paper can offer a valuable reference for the improvement of multi-objective reliability assessment theory.