In this study, we apply State Dependent Riccati Equation (SDRE) based optimal control technique to a nonlinear tumor growth model. The model consists of three biological cells which are normal tissue, tumor and immune cells. The effect of chemotherapy treatment is also included in the model. Chemotherapy administration is considered as a control input to the nonlinear cancer dynamics and the amount of administered drug is determined by using SDRE optimal control. The optimal control is applied to the model in order not only to drive the tumor cells to the healthy equilibrium state but also to minimize the amount of the drug used. In SDRE control design, we investigate the effects of different weighting matrices in the cost function to be minimized. Simulation results show that selection of state dependent weighting matrices can yield positive outcomes such as less drug administration or control of tumor growth in a shorter time period.