To learn more of the phase distributions in unperturbed human tumour cells is a prerequisite prior to understanding of those in the perturbed cells. The work is important in understanding the efficiency of anti-cancer therapy. In this paper we investigate the existence, uniqueness and growth rate of the solution to a mathematical model of unperturbed human tumour cell line. At first, we construct the solution of this mathematical model by the method of continuation of solution, and then show the solution is unique. Finally, we find that the growth rate of the solution with respect to time is faster than exponential function. The basic mathematical techniques used here are variation of parameters and upper and lower solutions for differential equations. These results allowed one to estimate the cells population in each phase at specific time while one does not have cells mitosis DNA distribution data and it can also be used to compare with the perturbed cell lines.
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