Seismic fragility analysis of structures such as bridges must consider not only the uncertainties in the loads to which the structure is subjected, but also the uncertainties in the physical properties of the structure due to deterioration and other factors. Since a bridge system consists of many components, the uncertainty parameters are extensive. Therefore, the number of calculations required for probability convergence in the commonly used Monte Carlo (MC) calculation is huge, and the cost is very high. Surrogate models, which reduce the computational cost by substituting machine learning for structural analysis, are attracting attention. This study proposes surrogate model building using deep kernel learning (DKL). A multilayer perceptron (MLP) is used in the feature extraction part of deep kernel learning to extract features from high-dimensional uncertainty parameters. In addition, a multi-output kernel is incorporated in the Gaussian process part to model the correlation between outputs. In the verification, a DKL surrogate model was constructed for the seismic fragility analysis of a multi-span curved bridge. As a result, the DKL surrogate model could evaluate seismic fragility at a low computational cost. In addition, the DKL surrogate model allowed us to determine which members contribute to the system fragility, which is not practically possible with conventional MC calculations.