The least square method and SPSS 22.0 are used to obtain three common parameter estimation formulas of the tumor growth model whether the maximum environmental capacity of tumor cells is known or unknown. Through the parameter estimation formula and the published data, the growth rates of 8 different types of cancers are calculated. The original data are fitted through Matlab. Furthermore, the fitting effect is verified by taking the first three quarters of the initial data of tumor cell growths as the fitting data and by taking the last quarter of the experimental data as the prediction data. The optimal mathematical models for describing various tumor growths are determined. According to the characteristics and the fitting effects of tumor growths, as well as the function characteristics of the organs where tumors are located, the growth situations of 8 types of cancer cells in different organs are classified from a mathematical perspective. Further, this study provides a theoretical reference for further research on the anti-tumor

immunity mechanism and the improvement of mathematical models for immune cells inhibiting tumor growths.