The intermittent and uncertain behavior of renewable energy sources; moreover, the increase in penetration of these resources causes some drawbacks in power grids, particularly in low-inertia microgrids. In addition to supply-side challenges, changing load rate has a considerable negative effect on small-size microgrids. Therefore, according to these challenges, the lack of balance between generation and demand is a vital issue in microgrids. One way to face these challenges would be using a suitable control strategy. In this research, an adaptive fuzzy model predictive control has been proposed as a novel control approach and has been compared with conventional controllers such as an optimal PI, and an adaptive optimal model predictive control. It is important to mention that, various types of load changing and time-varying parameters have been considered for a new model of small size microgrids in this study. The comparison and simulation results obviously indicate the effectiveness of the proposed control strategy.