A dynamic physical model of a microbial fuel cell (MFC) anode is presented and parameterized. It describes the evolution of current density and biofilm mass over time as a function of substrate concentration. The model is particularly useful for process monitoring or control purposes because it reproduces the dynamics of the MFC anode and contains comparatively few parameters. Parameters are identified using data from the response of the MFC to a substrate concentration pulse. Theoretical and practical identifiability of the parameters is evaluated, and parameter confidence intervals are determined.