Single phase Quasi Z Source Inverter (QZSI) can implement DC-DC and DC-AC conversion in single stage system, but it has double-line frequency ripple in DC side, which limits its application. This paper discusses the suppression of double-line frequency ripple of single-phase QZSI with active power decoupling. With the output reactive power of inverter, it proposes the analysis and derivation method of the phase legs' voltage and current stress when the power factor angle changes in the [-π/2，π/2] range. Based on the minimum voltage stress principle, the value of the new loop AC decoupling capacitor and its voltage reference value setting method are given, and the closed-loop control strategy is designed. Simulation and prototype experiments are shown to prove the correctness and effectiveness of the proposed method. This work is supported by National Natural Science Foundation of China (No. 51407122).