Obesity has become a severe threat to public health due to its causal link to various chronic diseases. It has been shown that the increase in circulating free fatty acids (FFAs) and its induction of chronic inflammation are key mechanisms of various diseases associated with obesity. For this system, it is known that adenosine monophosphate-activated protein kinase (AMPK) activity is repressed by the elevated level of FFAs, and this depression causes an elevation of pro-inflammatory cytokines such as tumor necrosis factor-α (TNFα), which indicates an inflammatory response. However, detailed mechanisms and dynamics of the FFA-induced inflammation are not well understood yet. In this study, a new dynamic model is constructed to describe how TNFα synthesis in macrophages is triggered by palmitate. which is a representative FFA. First, a set of ordinary differential equations is developed to describe how palmitate regulates the AMPK activity and the NFκB signaling pathway to construct a comprehensive dynamic model for the palmitate-induced TNFα expression. Second, in vitro experiments are conducted to measure the dynamics of key molecules involved in the process. Before these measurements are used to train the proposed model, global sensitivity analyses are performed to determine the most important parameters to avoid overfitting. Lastly, only the selected parameters are estimated by solving an optimization problem to calibrate the model. After estimating the selected parameters, the trained model shows a reasonable agreement with the experimental measurements, which validates the model predictions.