The introduction of the Z-source network in the distribution network can flexibly control the voltage and achieve high-efficiency conversion of electric energy. In order to analyze the model characteristics of the quasi-Z-source topology in detail, a small-signal model characteristic applied to the quasi-Z-source network in the distribution network by using the state-space method and the small-signal modeling method is proposed, analyzed and verified. Firstly, the state-space method is used to deduce the mathematical model of the quasi-Z-source network. Secondly, the transient analysis is carried out on the quasi-Z-source network by using the small-signal model, and the transfer functions of inductive current and capacitive voltage are obtained. In addition, the zero and pole distributions of the two transfer functions are analyzed in detail, and the characteristics of system stability are obtained. Finally, the results of the MATLAB/Simulink simulation and physical prototype experiments are presented for validating the proposed strategy.