The data collected by the bridge structure health monitoring (SHM) system is usually mixed with stochastic noise. It is of great significance to utilize reasonable method to denoise the monitoring data for decreasing the misjudgement in structural health diagnosis decisions. However, the error caused by multipath effect and stochastic noise is fully inextricable by traditional denoise methods. In view of this, a multi-filter denoising method, which combines the adaptive filtering based on LMS (AFLMS), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and wavelet transform (WT), is proposed in this paper. Firstly, the SHM strain data of a steel box girder bridge is primarily denoised by AFLMS, and then the signal is decomposed into a series of intrinsic mode function (IMF) components by CEEMDAN. Further, the IMF components are denoised by WT, and the processed components are restructured to obtain the final denoised signal. In addition, the effectiveness and superiority of the proposed method is verified by comparing the signal-noise ratio and root mean square error of the denoising signals acquired by WT and CEEMDAN-WT. On basis of this, the strain signals after denoising by the proposed method are analysed, and the evolution law of vibration frequency at the measuring point and the correlation of vibration frequency at different measuring points are investigated. As a result, the proposed method can provide a solid theoretical and technical foundation for damage identification and safety assessment of bridge structure, which has important scientific significance and broad application prospects.