<p>High-precision GNSS height time series prediction can provide a critical reference for applications such as regional or global reference frame maintenance, crustal movements, structural safety monitoring, and geological hazards. An improved ICEEMDAN-MPA-GRU model has been developed to achieve high-precision prediction results. The Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) is used to decompose the original time series, and subsequently the Gated Recurrent Unit (GRU) is employed for the forecast of the time series. Marine Predators Algorithm (MPA) is also included to optimize the parameters of the algorithms (e.g., number of neurons, learning rate, and iteration count). The ICEEMDAN-MPA-GRU model is applied to the daily height coordinate (Up component) of 14 GNSS stations in North American with time span of 20 years (2000.0–2020.0). A comprehensive evaluation was performed using the proposed Weighted Quality Evaluation index (WQE). The ICEEMDAN-MPA-GRU model achieved an average WQE of 0.463. Compared to the Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), MPA-GRU, and ICEEMDAN-MPA-LSTM models, the ICEEMDAN-MPA-GRU model reduced the prediction WQE by an average of 63.77%, 58.47%, 54.20%, and 30.09%, respectively. Furthermore, the ICEEMDAN-MPA-GRU model demonstrated strong robustness in the presence of data gaps.</p>