The dynamic prediction of bridge extreme stress based on health monitoring stress data was studied. Considering the monitored stresses’ periodicity， randomness， dynamic characteristics and so forth，firstly，the Fourier Dynamic Nonlinear Model（FDNM） of bridge monitored extreme stress was built，and， with Taylor series expansion technology， FDNM was approximately transferred into the Fourier Dynamic Linear Model（FDLM）；secondly， with Bayes method， the Bayesian FDLM（BFDLM） was built based on the monitored extreme stress data，and the one-step forward prediction distribution parameters of monitored extreme stress and distribution parameters of posterior stress state were dynamically predicted； finally， the monitored extreme stress data of an actual bridge was provided to illustrate the application and feasibility of the proposed models and methods. The results show that the proposed BFDLM can reflect bridge extreme stresses' periodicity， randomness， dynamics and so forth，which can provide the theoretical foundation and application approach for bridge monitoring extreme stress prediction.