This paper proposes a new method for improving the performance of grid-connected single-stage Quadratic Boost Inverters (QBIs). Compared to the other single-stage boosting inverters, such as ZSI, qZSI, and the basic SSI, QBI has several advantages. It combines the features of a quadratic dc-dc boost converter and Split-Source Inverter (SSI) to give a high voltage gain. As a result, it offers superior benefits in reducing the overall system's complexity, size, and cost. The grid-connected QBI is traditionally controlled via two control loops. The first loop regulates the dc-link voltage using a PI controller, while the second controls the current injected into a grid using the decoupled control approach. In this paper, a sliding mode controller (SMC) is proposed for the grid-side controller to achieve accurate and quick responses instead of using the decoupled approach that is based on PI controllers. The basic principles and detailed analysis of the proposed method are introduced. Moreover, comprehensive simulation results based on the actual parameters of a prototype have verified the overall control system and the advantages of the proposed SMC compared to the PI controller.