In this study, we present a Direct Model Reference Adaptive Control (DMRAC) algorithm in a boost converter used in islanded microgrids (MG) with a solar photovoltaic (PV) system. Islanded types of microgrids have very sensitive voltage and frequency variability; therefore, a robust and adaptive controller is always desired to control such variations within the MG. A DC–DC boost converter with a modified MIT rule controller is proposed in this paper, which stabilizes output voltage variations in islanded MG. Since the boost converter is a non-minimum phase, the controller design that relies only on output voltage feedback becomes challenging. Even though output voltage control can be achieved using inductor current control, such current mode controllers may also require prior knowledge of the load resistance and more states, such as output and inductor currents in feedback. Here, two control loops are used to achieve a stable output voltage; a PID controller can regulate the output voltage at a fixed level, and the outer loop is designed to implement the MIT rule for a DMRAC. To ensure that the actual system is following the desired reference model, using only an output voltage feedback sensor, a DMRAC is devised to update the PID controller parameters in real-time. Compared to a DC–DC boost converter connected to the MG, a controller, such as the one introduced in this paper, is more successful in dealing with unknown parameter fluctuations and disturbance changes. The MATLAB/SIMULINK is used to design and simulate the controller with different load disturbances and input voltage variances. The hardware validation is also carried out to show the performance of the proposed controller. Our results suggest that the DMRAC provides robust regulation against parameter variations.