This paper compares two finite-control-set model predictive control (FCS-MPC) strategies in the context of a grid-connected single-phase quasi-Z source inverter (SP-qZSI). Both schemes use discrete-time models of the inductor current and capacitor voltage for the DC side, as well as the output current on the AC side. To enhance the converter’s performance, given the non-minimum phase characteristics of the DC side, a long prediction horizon is implemented for the predictive control. However, a horizon of this nature can be highly demanding in terms of processing load, rendering it inapplicable for some microcontrollers. To address this issue and mitigate the processing load, an alternative control strategy is presented that divides the total number of candidate solutions to be evaluated into smaller segments. The performance of the two control strategies is compared using total harmonic distortion (THD) and simulation times as evaluation metrics. The results indicate that the proposed strategy achieves significantly shorter simulation times than the compared control strategy when increasing the prediction horizon. Additionally, a reduction in the THD was observed in the proposed strategy, reaching an average of 2.8%, which is lower than the compared strategy that exhibited THD close to 3.5%.