Background and objectiveNF-κB can be activated by the canonical and non-canonical pathways. These two pathways interplay via the TRAF1|NIK complex after stimulation by TNF. However existing mathematical models of two pathways are inadequate. In this context, an improved mathematical model is constructed to simulate these two pathways and their coupling stimulated by TNF. MethodsA schematic description of two NF-κB pathways and their relation after TNF stimulation is constructed at first. Then twenty-eight ordinary differential equations are utilized to build the mathematical model. Model equations are solved via the ordinary differential equation solver (ode23). ResultsThe proposed model firstly reconstructs the changes in concentrations of NF-κB pathway related biochemical factors with time, and further investigates the underlying mechanism of interaction between two pathways through the TRAF1|NIK complex after stimulation. ConclusionsThe model is validated through good agreement between simulation results and published experimental observations. This study helps to well understand the canonical and non-canonical pathways and their interaction. It also provides a potential tool to investigate how the dysregulated pathways act in pathological conditions.