Considers a problem of stabilizing a mathematical model of HIV dynamics is considered. The problem of construction of feedback control, which stabilizes the HIV model. The mathematical model described by a system of linear functional differential equations, which allows you to apply for building construction management, the theory of analytical design of controllers for systems with delays. The model is described by a system of functional differential equations. A stabilizing control is constructed basing on the method of explicit solutions of Generalized Riccati’s Equations of the theory of analytical constructing regulator for systems with delays. For construct a feedback control we use the variant of explicit solutions of the generalized Riccati’s equations (the study of control stabilizing properties based on other variants discussed in previous authors articles). Stabilizing control for the system of differential equations with delay supports HIV-infection model spread at a certain sufficiently small non-zero level. Results of the research can be applied to analysis of some aspects of HIV dynamics.