Secondary frequency control is crucial for ensuring frequency stability in islanded microgrids. To address potential control inefficiencies arising from different sampling rates across microgrid subareas, this paper investigates corresponding control scheme based on multi-rate sampling data. Compared to existing schemes, the proposed method explicitly considers multi-rate sampling scenarios when constructing the system mathematical model. On the one hand, this enhances the generality and practical applicability of the control scheme. On the other hand, by shortening the sampling intervals in subareas with sufficient communication resources, larger sampling intervals can be adopted in subareas with relatively constrained communication resources, thereby avoiding data congestion during transmission. In stability analysis and feedback gain design, this paper introduces the looped-functional approach to relax the positive definiteness requirement of the Lyapunov functional, thereby reducing the conservatism of the results. Finally, simulation studies are conducted to verify the effectiveness of the proposed scheme.