A microgrid formed by a cluster of parallel distributed generation (DG) units is capable of operating in either islanded mode or grid-connected mode. Traditionally, by using model predictive control algorithms, these two operation modes can be achieved with two separate and different cost functions, which brings in control complexity and hence, compromises system reliability. In this article, a unified model predictive voltage and current control strategy is proposed for both islanded and grid-connected operations and their smooth transition. The cost function is kept unified with voltage and current taken into account without altering the control architecture. It can be used for high-quality voltage supply at the primary control level and for bidirectional power flow at the tertiary control level. In addition, by only using DGs' own and neighboring information, a distributed fuzzy cooperative algorithm is developed at the secondary layer to mitigate the voltage and frequency deviations inherent from the power droop. The fuzzy controller can optimize the secondary control coefficients for further voltage quality improvement. Comprehensive tests under various scenarios demonstrate the merits of the proposed control strategy over traditional methods.