The wide use of inverters in microgrids motivates the development of digital controllers with sampling systems. This paper proposes a multi-rate sampling frequency and voltage regulation method for inverters-based distributed generators (DGs). The fast-sampling signals are adopted to achieve the primary control, which is composed of the VSG-based frequency control and the voltage droop control with a low-pass filter (LPF). Based on the unified primary control model, the low-sampling distributed model predictive control (DMPC) is proposed as secondary frequency and voltage control. Considering the microgrid network, the inverter-based DGs supply power for both the local load and loads on other buses. The proposed DMPC method can overcome the disproportionate impedances of interconnecting lines among buses. Then the frequency and voltage of islanded microgrid can be restored to rated values with accurate power sharing. The DMPC-based secondary control and the primary control have different sampling rates. The stability and dynamic performance of the proposed multi-rate sampling control system are investigated for the first time. Finally, both simulation and experiment tests are carried out to validate the effectiveness of the proposed control strategy.