The quasi-Z source inverter (qZSI) has a unique impedance network that couples the power supply to the conversion circuit and has a special buck-boost function. Inductors are the core components of the impedance network, which occupy a large proportion of qZSI, and thus the size and weight of the two inductors can be significantly reduced by a coupled inductor design. In this paper, a novel design of coupled inductor is proposed to reduce the input current ripple of qZSI. Then, the loss of the coupled inductor and the temperature rise are analyzed. Moreover, the analytical expressions of the loss and temperature of the magnetic core and the winding are derived. A multiphysics model using the finite element software Ansys and a 6 kW qZSI prototype were built for simulation and verification.