Because cancer usually involves multiple genes and pathways, combination therapy is considered as a promising approach for cancer treatment. However, when multiple drugs are taken by a patient simultaneously, toxicity becomes a concern. A potential solution is to give the drugs sequentially rather than simultaneously. In this study, we try to explore the feasibility of such an approach. Specifically, this study investigates the response of genetic regulatory networks to sequential (switched) drug inputs. The switching mechanism is based on the combination of a state-dependent and time-driven switching function. The design of the switching strategy ensures that the genetic regulatory network will be stabilized and satisfies a decay rate performance index. Simulation results using a mTOR pathway model show the effectiveness of the proposed method.