The energy storage quasi-Z-source cascaded H-bridge (ES-qZS-CHB) multilevel converter has the features of high reliability and sound output voltage quality, allowing it to inject intermittent and random fluctuations of solar energy into the grid smoothly and efficiently. For a grid-connected energy storage quasi-z source multilevel converter to operate efficiently, it must have a low switching frequency. However, typical finite control set model predictive control (FCS-MPC) creates voltage and current prediction errors when functioning with a low sampling frequency, parameter mismatch, model discretization, and sampling error. To address this issue, an enhanced FCS-MPC method based on a steady-state error compensation mechanism is presented to reduce the steady-state error of MPC at the low sampling frequency and realize the output equalization power of each module of the cascaded H-bridge converter. Finally, the experimental results of a single-phase, three-cell (seven-level), quasi-z-source cascaded H-bridge multilevel inverter for energy storage quasi-z-source support the theoretical analysis and proposed approach.