An indirect model predictive control (iMPC) approach is proposed for regulating a grid current waveform provided by a single-phase inverter connected to a distorted grid. An algorithm implemented in the control system takes into account a significant computational delay. The distorted grid with the 5th harmonic is considered, which imposes additional restrictions on the iMPC and phase-locked loop utilization. Hardware setup involves a three-level neutral point clamped inverter and an inductive output filter. From a finite set of modulation index values, the iMPC current control selects one value for an external fixed switching frequency driver based on the LS-PWM strategy. Relevant cost function composition and modulation index regulation for improvements of transient and steady-state responses are discussed. Simulation and experimental verification is presented.