We present an optimal control strategy for nonlinear systems with application to the drug therapy of cancer. The tumour growth model is represented by a system of equations from population dynamics which is based on the competition between normal cells and tumour cells. The effect of the immune system in the presence of cancer is also included in the model. A linear time varying approximation technique is proposed to construct an optimal control strategy for the nonlinear system which is valid not only within small perturbations around the equilibrium point, but also for global dynamics of the system. The optimal control method is applied to eliminate the tumour cells whilst minimizing the amount of drug in the simulated model. Simulation results show that cancer cells can be 'eradicated'(1) in a very short time with a small amount of drug using an optimal administration of the therapy. (C) 2009 Elsevier Ltd. All rights reserved.