Realizing local voltage regulation and powersharing of an islanded AC microgrid can be achieved by conventional control that employs outer-loop droop control and inner-loop cascaded linear control. However, it has limited dynamic response, complex structure, and a rapid rate of change of frequency. In addition, the use of two-stage DC-DC-AC converters for interfacing the renewable energy sources and the microgrid reduces the system efficiency. The split-source inverter (SSI) introduces an alternative single-stage solution for the DC-DC-AC conversion. This paper proposes a virtual synchronous generator (VSG) control algorithm based on model predictive control (MPC) for a three-phase SSI. A finite-set MPC (FS-MPC) is employed to achieve a simple control structure, fast dynamic response, higher stability, and improved current limitation in the inner control loop. A VSG control algorithm without a phase-locked loop is utilized in this paper to achieve active-power-sharing and inertia emulation in the outer control loop. The analysis and modeling of the proposed technique are presented in detail. The simulation results verified the merits of the analysis and the theoretical finding.