Objective The fermentation medium contains many complex components (vitamins, minerals, etc.) for better growth of the microorganisms. The increasing purity and number of these components used in the medium seriously affect the cost of the microbial process. This study aimed to further optimize the concentration of the components used in the medium (yeast extract and peptone) for inulinase fabrication by Aspergillus niger from sugar-beet molasses in shake flask fermentation by using Central Composite Design (CCD) and to kinetically identify the fermentation. Results The results indicated that the optimal medium composition consisted of only 4.2% (w/v) yeast extract. By using the fermentation environment, the inulinase generation, inulinase/sucrase ratio, maximum inulinase generation rate, maximum sugar depletion rate, and substrate utilization yield were determined as 1294.5 U/mL, 1.2, 159.6 U/mL/day, 7.4 g/L/day, and 98.1%, respectively. The kinetic analysis of the fungal development (logistic model) indicated that a specific development rate and initial biomass concentration were 0.89/day and 1.79 g/L, respectively. Inulinase and sucrase productions are mixed-development associated since the alpha value not equal 0 (8.46 and 4.31 U/mgX) and the beta value not equal 0 (5.15 and 4.83 U/mgX day), respectively (Luedeking-Piret model). Besides, the maintenance value (Z) (0.009 gS/gX day) was lower than gamma value (1.044 gS/gX), showing that A. niger commonly uses the substrates for enzyme fabrication and fungal development (modified Luedeking-Piret model). Conclusions The enzyme activity was increased by optimizing the concentration of the components used. It was demonstrated that the proposed kinetic models can victoriously define fungal development, enzyme fabrication, and sugar depletion.