Signal processing is one of the essential components in vibration-based approaches and damage detection for structural health monitoring. Since signals in the real world are often nonlinear and non-stationary, especially in extended and complex structures, such as bridges, the Hilbert–Huang transform is used for damage assessment. In recent years, the empirical mode decomposition technique has been gradually used in structural health monitoring and damage detection. In this article, the application of complete ensemble empirical mode decomposition with adaptive noise technique is investigated to identify the presence, location, and severity of damage on a steel truss bridge model. The target is built at laboratory conditions and experimentally subjected to white noise excitations. By employing complete ensemble empirical mode decomposition with adaptive noise technique, four key features extracted from the intrinsic mode functions, including energy, instantaneous amplitude, unwrapped phase, and instantaneous frequency, are assessed to localization, quantification, and detection of damage both quantitatively and qualitatively. In addition, to further explore the sensitivity of the damage detection approach based on the complete ensemble empirical mode decomposition with adaptive noise technique method, several improved damage indices are proposed based on the combinations of two statistical time-history features, including kurtosis and entropy features with the energy and instantaneous amplitude features of the analyzed signal. The experimental results from the damage indices based on the extracted features demonstrate the robustness, superiority, and more sensitivity of the complete ensemble empirical mode decomposition with adaptive noise technique method in addressing the damage location, classifying the severity, and detecting the damage compared to empirical mode decomposition and ensemble empirical mode decomposition techniques.