Binary/multiple substrates are sometimes encountered during fermentation processes. The Monod, Luong, Haldane, Andrews, and Aiba models are commonly used in bioprocesses, and such models are limited to predictions of the growth rate of microorganisms for single substrate systems. This study proposes a new model that can predict the growth rate of microorganisms for binary or multiple substrates as well as the simultaneous profiles of substrates, cells, and products during fermentation. The experimental case in this work is an aerobic fermentation of date’ syrup containing glucose, fructose, and small amounts of sucrose to yield cell mass from glucose with minimal fermentation of fructose using Saccharomyces cerevisiae ATCC 36858. The substrate with a slower rate of consumption, i.e., fructose was demonstrated to inhibit cell growth. The generalized kinetic model included the novel inhibition by the fraction of the second substrate, i.e., fructose that was revealed in the fermentation process as indicated by two exponential growth rates. The proposed model accounts for substrate and product inhibition. The applicability of the model to multi-substrate fermentation was demonstrated by predictive data from published literature and our laboratory; the calculated regression factor (R2) was in the range of 0.91-0.99 for all tested data.