Interleukin-12 is a pro-inflammatory cytokine which promotes Th1 and cytotoxic T lymphocyte activities, such as Interferon- secretion. For this reason Interleukin-12 could be a powerful therapeutic agent for cancer treatment. However, Interleukin-12 is also excessively toxic. Interleukin-27 is an immunoregulatory cytokine from the Interleukin-12 family, but it is not as toxic as Interleukin-12. In recent years, Interleukin-27 has been considered as a potential anti-tumor agent. Recent experiments in vitro and in vivo have shown that cancer cells transfected with IL-27 activate CD8+ T cells to promote the secretion of anti-tumor cytokines Interleukin-10, although, at the same time, IL-27 inhibits the secretion of Interferon- by CD8+ T cells. In the present paper we develop a mathematical model based on these experimental results. The model involves a dynamic network which includes tumor cells, CD8+ T cells and cytokines Interleukin-27, Interleukin-10 and Interferon-. Simulations of the model show how Interleukin-27 promotes CD8+ T cells to secrete Interleukin-10 to inhibit tumor growth. On the other hand Interleukin-27 inhibits the secretion of Interferon- by CD8+ T cells which somewhat diminishes the inhibition of tumor growth. Our numerical results are in qualitative agreement with experimental data. We use the model to design protocols of IL-27 injections for the treatment of cancer and find that, for some special types of cancer, with a fixed total amount of drug, within a certain range, continuous injection has better efficacy than intermittent injections in reducing the tumor load while the treatment is ongoing, although the decrease in tumor load is only temporary.