Understanding the deformation behaviors of hydraulic tunnels during excavation is the premise of designing excavation support schemes. Conventional numerical simulation methods are time consuming, and usually involve a large amount of computations when predicting tunnel excavation deformation behaviors. To overcome these difficulties, we adopted a three-parameter exponential function to characterize the tunnel excavation deformation curve, and proposed a surrogate model-based method capable of rapidly predicting tunnel excavation deformation behaviors, using the Latin hypercube sampling (LHS) method and the Kriging model. Then the implementation process of this method was discussed in detail. Taking a typical water conveyance tunnel project as the case study, we established a rapid prediction surrogate model to predict the deformation characteristic curves for three typical tunnel sections, with the buried depth and mechanical parameters of the surrounding rock as the input, and the deformation characterization parameters as the output. The results show that the model prediction is in a good agreement with that of the finite element simulation analysis, validating the prediction accuracy and adaptability of the proposed method. Compared with conventional numerical simulation methods, the proposed method can greatly improve the prediction efficiency of the excavation deformation behaviors of hydraulic tunnels.