A novel controller design approach is developed to determine personalized chemotherapy drug delivery protocols for cancer treatment. The methodology combines successive approximation approach for optimal control and model reference adaptive control to realize the proposed drug administration scenario for patients without prior knowledge of model parameters in the nonlinear cancer dynamics. Although many approaches have been proposed to determine the optimal drug delivery protocol for eradicating tumor in the nonlinear cancer model, the main shortcoming of these approaches is the requirement of nonlinear model dynamics, which is unknown to physicians in reality. To overcome this deficiency, we first determine the optimal drug delivery protocol for a reference patient with known mathematical model and parameters via successive approximation approach technique. Then, using the proposed approach, we adapt the reference patient's drug administration scenario to unknown cancer patients by suggesting a new adaptation mechanism for the unknown nonlinear plant dynamics. An efficient and robust approach is proposed here for the physicians to prescribe a personalized chemotherapy protocol for a cancer patient by regulating the drug delivery protocol of a reference patient. The efficacy of the proposed algorithm in eradicating the tumor lumps with different sizes in several patients is verified using numerical simulations in which the unknown parameters are randomly selected in the Monte Carlo approach.