The study of DC microgrids has become an important research topic due to its advantages in terms of efficiency, reliability and controllability. In this paper, an adaptive optimal control approach is proposed for primary-secondary control in DC micro-grids under master-slave operation. Stability elimination of voltage deviations is guaranteed, through current control and recursive least squares for identifying the dynamic model. In addition, a linear-quadratic regulator (LQR) with integral action is proposed to improve the stability of the microgrid in a masterslave configuration. Simulation results on a realistic test system demonstrate the advantages of the proposed control.