This article proposes a new continuous input quadratic buck-boost converter. The proposed converter consists two simultaneously operated active switches with two diodes and fourth-order energy storing elements. This article explains the converter operation with time-domain key waveforms, voltage conversion ratio, electric stress of the power switching devices, designing circuit parameters and boundary conditions, the non-ideal voltage gain. Further, the comparison is made with other buck-boost converters with regard to voltage gain and effectiveness index. MATLAB-based simulations are conducted for step-up (boost) and step-down (buck) modes of operation of the new converter to validate the performance. The advantages like continuous input, wide range voltage gain and higher power density make the new converter is suitable for renewable power generation.