This paper proposes a direct model predictive control (DMPC) technique for grid connected four-leg quasi-Z-Source Inverters (qZSIs). Due to drawbacks of two-stage Voltage Source Inverter (VSI) and Boost Converter systems, a three-phase four-leg single stage qZSI is proposed. Despite of the single-stage buck-boost capability, qZSI needs to be controlled for both DC and AC sides. Therefore, DMPC technique is proposed as it can incorporate multiple control loops in one control law. Furthermore, four-leg topology is proposed to deal with the unbalanced load conditions and to ensure a high power quality for grid. Simulation results using Matlab-Simulink and a 10kW QZSI are presented to verify the feasibility of the proposed control algorithm.