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Objective: To setup a three‐component tumor growth mathematical model and discuss its basic application in tumor fractional radiotherapy with computer simulation. Method: First, our three‐component tumor growth model extended from the classical Gompertz tumor model was formulated and applied to a fractional radiotherapy with a series of proper parameters. With the computer simulation of our model, the impact of some parameters such as fractional dose, amount of quiescent tumor cells, and α/β value to the effect of radiotherapy was also analyzed, respectively. Results: With several optimal technologies, the model could run stably and output a series of convergent results. The simulation results showed that the fractional radiotherapy dose could impact the effect of radiotherapy significantly, while the amount of quiescent tumor cells and α/β value did that to a certain extent. Conclusions: Supported with some proper parameters, our model can simulate and analyze the tumor radiotherapy program as well as give some theoretical instruction to radiotherapy personalized optimization. [ABSTRACT FROM AUTHOR]