The two inductor current boundaries are derived, and segmented smooth iteration mapping model of current controlled quadratic boost converter is established based on the detailed description of switching states. The comparative analyses of the nonlinear bifurcation behaviors are performed with input inductor current and the storage inductor current as current feedback respectively. Two boundary conditions for the transition from stable period-one state to sub-harmonic oscillation state and for the transition from discontinuous conduction mode to continuous conduction mode are derived by analyzing stability and operation mode. The operation-state regions corresponding to circuit parameter regions are estimated by utilizing the parameter-space maps. An experimental circuit is built and the results show that both different bifurcation routes and operation mode transition phenomenon are changed with parameter variation, the current controlled quadratic boost converter exhibits complicated dynamical behaviors. The experimental results verify the correctness of the theoretical analysis.