Bridges are critical to economic and social development of a country. In order to ensure the safe operation of bridges, it is of great significance to accurately predict displacement of monitoring points from bridge Structural Health System (SHM). In the paper, a CEEMDAN-KELM model is proposed to improve the accuracy of displacement prediction of bridge. Firstly, the original displacement monitoring time series of bridge is accurately and effectively decomposed into multiple components called intrinsic mode functions (IMFs) and one residual component using a method named complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Then, these components are forecasted by establishing appropriate kernel extreme learning machine (KELM) prediction models, respectively. At last, the prediction results of all components including residual component are summed as the final prediction results. A case study using global navigation satellite system (GNSS) monitoring data is used to illustrate the feasibility and validity of the proposed model. Practical results show that prediction accuracy using CEEMDAN-KELM model is superior to BP neural network model, EMD-ELM model and EMD-KELM model in terms of the same monitoring data.