Abstract: Uncertainty quantification (UQ) is to quantify the uncertainty in the structural response propagated from the parameter uncertainty of a structure. The traditional Monte Carlo simulation (MCS) requires a large number of numerical computations, which is time-consuming and thus may be impractical for UQ of large and complex structures. The surrogate model method builds an approximate mathematical model using a small set of training samples to replace the original numerical model, thus improving the computational efficiency. To address the problems of high cost for high-fidelity samples and low accuracy for low-fidelity samples, this paper proposes a generalized co-Gaussian process model (GC-GPM) integrating high- and low-fidelity training samples. Within the GC-GPM framework, the expressions of the mean and variance of the structural response can be analytically obtained. Three examples of the spatial structures are used to verify the effectiveness of the GC-GPM-based UQ method, and the MCS, co-GPM, and GPM are used for comparison. It can be concluded that the GC-GPM method proposed has advantages of high computational accuracy and efficiency.