<p>Melanoma is one of the most aggressive types of cancer. Although it has a low percentage of incidence in the population, a high degree of lethality is observed due to its rapid metastasis. As melanoma is a highly immunogenic cancer, it has been used as an experimental model in several studies aimed at developing therapies, such as immunotherapy with Chimeric Antigen Receptor (CAR) T-cells. We propose a mathematical model of three ordinary differential equations to describe the dynamics of melanoma in the presence of Tumor-Associated Macrophages (TAMs) and CAR T-cell therapy, to assess the role of TAMs cells in the failure of this melanoma therapy. We examine the existence and asymptotic stability of equilibrium points of this system, giving a biological interpretation to each of them. Based on our theoretical and numerical results, we conclude that immunosuppression has a negative impact on CAR T-cell immunotherapy and that increasing the immunotherapy dose can improve tumor control. Furthermore, an increase in the action of the TAMs population on tumor proliferation can induce oscillations that eventually become periodic.</p>