Enzymes are biodegradable catalysts naturally present in living organisms. Enzymes can accelerate biochemical reactions by reducing the activation energy, and they are not consumed during reaction processes. Numerous applications of enzymes have been developed in biotechnology, industry, medicine, pharmaceuticals, food processing, biofuels, and so on. In this study, we develop a mathematical model describing enzymatic reactions with a Ping-Pong mechanism and competitive substrate inhibition. In order to obtain insights into the model behaviors, we use Python software to obtain numerical solutions for the model. Some discussions on the numerical results is provided. Finally, we briefly discuss a potential application of the model and some future work.