This article studies the design and implementation of multi-objective predictive control (MO-PC) of a grid-connected seven-level packed U-cell (PUC7) inverter for minimising the line current total harmonic distortion (THD) and capacitor voltage error simultaneously. The weighting factor method is usually used as a simple method for solving the control problem in the literature. However, there are some difficulties and shortcomings in the calculation of weighting factors. Here, max-min selection strategy with together priority is adopted to reduce these deficiencies and improves the system performance. The switch model of the PUC inverter is derived and then applied in designing the MO-PC for grid-connected applications, where a controlled active or reactive power is injected into the utility. A comparative study among three strategies of weighting factor, fuzzy decision-making and max-min selection is performed to distinguish the proposed method superiority. Experimental results are given to validate the practicality of the applied controller in regulating the line current and capacitor voltage of the grid-connected PUC7 inverter.@en