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This study devises an advanced small-signal based approach (SSA) to model high-order power converter system (HOPCS); in detail, a 3-Z-network converter which employs a single switch to achieve high voltage gain is utilised as a typical example of HOPCS. Therein, four operating modes are detailed in terms of the states of electric current flowing through the inductors. The proposed SSA is performed by means of the state-space averaging technique and small-signal equivalent circuits in frequency domain. Based on the proposed approach, the derived transfer functions for input voltage, output voltage and control input yield deep insight into the dynamic responses of the converter in each working mode. In order to well validate the effectiveness of the proposed approach, numerical results and experimental prototype are conducted and measured, the results agree well with the theoretical analyses.