For the purpose of improving the fungal production of flavonoids, the influence of naphthaleneacetic acid (NAA) and coumarin on flavonoid production by fungus Phellinus sp. P0988 was investigated by developing the corresponding kinetics of flavonoid production in a 7-L bioreactor. Phellinus sp. was confirmed to form flavonoids in pellets and broth when cultivated in basic medium, and the optimum concentration of NAA and coumarin in medium for flavonoid production were determined to be 0.03 and 0.02 g/L, respectively. The developed unstructured mathematical models were in good agreement with the experimental results with respect to flavonoid production kinetic profiles with NAA and coumarin supplementation at optimum levels and revealed significant accuracy in terms of statistical consistency and robustness. Analysis of these kinetic processes indicated that NAA and coumarin supplementations imposed a stronger positive influence on flavonoid production and substrate consumption compared to their effects on cell growth. The separate addition of NAA and coumarin resulted in enhancements in final product accumulation and productivity, achieving final flavonoid concentrations of 3.60 and 2.75 g/L, respectively, and glucose consumption showed a significant decrease compared to the non-supplemented control as well. Also, the separate presence of NAA and coumarin respectively decreased maintenance coefficients (M (s)) from 2.48 in the control to 1.39 and 0.22, representing decreases of 43.9 and 91.1 %, respectively. The current study is the first known application of mathematical kinetic models to explore the influence of medium components adding on flavonoid production by fungi.