The Z-source inverter (ZSI) is a recently proposed single stage converter topology with buck-boost capabilities. The quasi-Z-source inverter (qZSI) has been developed which features several improvements when compared to the traditional ZSI. Control strategies of the ZSI and qZSI are important issue and several feedback control strategies have been investigated so far. This paper presents a model predictive control (MPC) of a grid connected qZSI, where the grid current is properly controlled during transient and steady state operation by including inductor current, capacitor voltage as well as switching frequency as additional control constrains. Both steady-state and transient results show high performance response of the proposed control technique. © 2013 IEEE.