The settlement and deformation of CFRD are caused by multiple complicated environmental factors, and the observed deformation data show obvious characteristics of noise interference, which has a great influence on the fitting and prediction accuracy of mathematical models; however, the useful signal and noise in the original signal can be decomposed effectively by wavelet transform theory. Therefore, the wavelet transform theory is introduced to establish a mathematical model based on wavelet threshold denoising, which is then applied to the denoising of the measured settlement data of a CFRD, and the denoised data is processed by Gaussian process regression (GPR) to establish a model for predicting settlement deformation of CFRD. Based on the measured settlement deformation data of a certain CFRD , the Wavelet-GPR model is used to fit and predict the dam settlement, and the calculation results are compared with those of the GPR model without denoising. The results show that the residual difference between predicted values and observed values of the Wavelet-GPR model is in accord with normal distribution. The RMSE of the learning segment decreased from 0.928 7 mm to 0.457 7 mm, and the MAE decreased from 0.485 0 mm to 0.330 6 mm after denoising. Furthermore, the RMSE of the prediction segment decreased from 1.308 9 mm to 0.917 6 mm, and the MAE decreased from 0.926 3 mm to 0.730 3 mm after denoising. After denoising, the proportion of sample observed values that fall in the 95% confidence range of the predicted values of the model is significantly increased. Therefore, the application of wavelet threshold denoising to the measured settlement data can reduce the error between the observed values and the actual values caused by noise, and the Wavelet-GPR model is practical and reliable in predicting the settlement deformation of CFRD.