GNSS (global navigation satellite system) vertical time series have the characteristics of non-stationary, non-linear, and noisy. Based on the in-depth study of the Prophet prediction model, and the good predictive effect of Prophet prediction model on trend signals and periodic signals, a “noise reduction-decomposition-prediction” combined prediction method of GNSS vertical time series that introduces EMD (empirical mode decomposition) was proposed. EMD denoising was performed on the original time series, the denoised series were decomposed and predicted, and the predicted signal of each component was reconstructed into the final predicted series. The measured vertical data was used for research, and results show that the average signal-to-noise ratio of the signal after noise reduction is 10.30 dB, and the average energy percentage is 88.75%; using the short-term prediction method, the root-mean-square errors of GNSS vertical time series prediction results are increased by 26.41% and 14.88% on average, respectively; the average percentage errors are increased by 18.92% and 7.91% on average, respectively, and the effectiveness and practicability of the combined forecasting method are verified.