Abstract: In this study, the fractional order of tumor cell growth and their interactions with effectors such as cytotoxic T-cells, E1(t) and natural killer cells E2(t) are studied. The Adam-Bashforth-Moulton algorithm is used 1 2 to numerically solve and simulate the model of the tumor immune system with fractional order. From the observation of the numerical result, reduces " from 1-0.75, decrease the maximum of tumor cells. Numerical simulations illustrate that the fractional-order derivative enriches the dynamics of the system and increases the complexity of the observed behaviors which confirms that the fractional-order may play the role of memory in the system.