In this paper, a high-gain low-switching-stress coupled-inductor with high voltage step-up voltage multiplier cells quadratic boost converter (VMC-QBC) is proposed. The turn ratio of the coupled inductors and the switch duty cycle increase the dynamic gain, and the two degrees of freedom adjustment and modularity of the voltage multiplier cells (VMC) make the structure more flexible. The use of the same drive signal for both switches makes control easier. While achieving multi-stage boosting and multiplication boosting from low to medium duty cycle, the passive clamping circuit absorbs the energy leaked by the coupled inductor, thus reducing the stress on the switching tube and alleviating the diode reverse recovery problem. A non-ideal model with parasitic parameters is developed to analyse the real voltage gain and the converter losses to give design guidelines. A 300 W prototype is designed and tested. The state space model of the converter is established and the working principle is analysed. Compared to other high-gain quadratic boost converters, the proposed converter has continuous input current, common ground characteristics, and high voltage gain at low to medium duty cycles to accommodate integrated multi-energy storage systems.