In this article, a high-gain bidirectional quadratic dc-dc converter is proposed. This converter is studied under step-up and step-down modes. In each power flow direction, two switches and two antiparallel diodes of the other switches operate. Therefore, the switching losses depend only on the operation of two switches in each direction. The use of coupled inductor in the proposed converter significantly reduces the input and output current ripples of the step-up and step-down modes, respectively, at all operating points of continuous and discontinuous conduction modes (CCM and DCM). The voltage gain of the proposed converter in the step-up mode is as high as that of the cascaded boost converter, and in the step-down mode, the converter voltage gain is similar to that of the cascaded buck converter. Thus, the high-voltage conversion ratio with an appropriate duty-cycle in both power flow directions can be achieved. The operating principles and steady-state analysis of the proposed converter in CCM, DCM, and the boundary-conditions between these modes are discussed in detail. Finally, a prototype of the converter is implemented in the laboratory and the experimental results are presented to validate the effectiveness of the proposed converter.