In this paper, we construct an infection-age model to study the interaction between viruses and the immune system within the host. In the model, the mortality rate of infected cells, the rate that cytotoxic T lymphocytes (CTL) kill infected cells, the rate that infected cells produce new virus, and the CTL proliferate rate may depend on the infection-age. The basic reproduction number and the threshold for the existence of steady states are obtained. Local stability of both the infection-free and infection steady states is studied by analyzing the linearized systems. Global stability of the infection-free steady state is obtained by investigating a renewal integral equation and global stability of the infection steady state is obtained by constructing a Liapunov functional. Numerical simulations are presented to verify the theoretical results.