Abstract: Engineering structure parameters are unavoidably subjected to uncertainty. It is important for structural analysis and design to quantify the sensitivity of structural uncertain parameters. Global sensitivity analysis (GSA) is an effective approach to evaluate the sensitivity of uncertain parameters. However, the widely used Monte Carlo simulation (MCS) may be impractical for GSA of complex structures because it needs a large number of runs of the expensive finite element model to obtain a confident estimate of the sensitivity indices. The generalized co-Gaussian process surrogate model (GC-GPM) integrates high- and low-fidelity training samples, which has advantages of high computational accuracy and efficiency. This paper proposes an analytical GSA method based on GC-GPM, which converts high-dimensional integrals into one-dimensional integrals. The sensitivity indices can be analytically obtained. The effectiveness of the proposed analytical GSA method is verified with four-parameter function and borehole function, and the MCS is used for comparison. It can be concluded that the GC-GPM based GSA method has advantages of high computational accuracy and efficiency. Finally, the proposed method is applied to the GSA of the stability of a reticulated shell structure, and the sensitivities of structural uncertain parameters are effectively assessed.