This research develops a new mathematical modeling method by combining industrial big data and process mechanism analysis under the framework of generalized additive models (GAM) to generate a practical model with generalization and precision. Specifically, the proposed modeling method includes the following steps. Firstly, the influence factors are screened using mechanism knowledge and data-mining methods. Secondly, the unary GAM without interactions including cleaning the data, building the sub-models, and verifying the sub-models. Subsequently, the interactions between the various factors are explored, and the binary GAM with interactions is constructed. The relationships among the sub-models are analyzed, and the integrated model is built. Finally, based on the proposed modeling method, two prediction models of mechanical property and deformation resistance for hot-rolled strips are established. Industrial actual data verification demonstrates that the new models have good prediction precision, and the mean absolute percentage errors of tensile strength, yield strength and deformation resistance are 2.54%, 3.34% and 6.53%, respectively. And experimental results suggest that the proposed method offers a new approach to industrial process modeling.