A nonautonomous mathematical model of chemotherapy cancer treatment with time-dependent infusion concentration of the chemotherapy agent is developed and studied. In particular, a mutual inhibition type model is adopted to describe the interactions between the chemotherapy agent and cells, in which the chemotherapy agent is modeled as the prey being consumed by both cancer and normal cells, thereby reducing the population of both. Properties of solutions and detailed dynamics of the nonautonomous system are investigated, and conditions under which the treatment is successful or unsuccessful are established. It can be shown both theoretically and numerically that with the same amount of chemotherapy agent infused during the same period of time, a treatment with variable infusion may over perform a treatment with constant infusion.