In this article, a novel propagative broad learning approach is proposed for nonparametric modeling of the ambient effects on structural health indicators. Structural health indicators interpret the structural health condition of the underlying dynamical system. Long-term structural health monitoring on in-service civil engineering infrastructures has demonstrated that commonly used structural health indicators, such as modal frequencies, depend on the ambient conditions. Therefore, it is crucial to detrend the ambient effects on the structural health indicators for reliable judgment on the variation of structural integrity. However, two major challenging problems are encountered. First, it is not trivial to formulate an appropriate parametric expression for the complicated relationship between the operating conditions and the structural health indicators. Second, since continuous data stream is generated during long-term structural health monitoring, it is required to handle the growing data efficiently. The proposed propagative broad learning provides an effective tool to address these problems. In particular, it is a model-free data-driven machine learning approach for nonparametric modeling of the ambient-influenced structural health indicators. Moreover, the learning network can be updated and reconfigured incrementally to adapt newly available data as well as network architecture modifications. The proposed approach is applied to develop the ambient-influenced structural health indicator model based on the measurements of 3-year full-scale continuous monitoring on a reinforced concrete building.