Abstract: Compared with active piecewise linear(PWL) and cubic smooth memristor model adopted in most memristor-based chaotic circuits, charge-control quadratic memristor model is more practical, which is derived from a passive device fabricated by HP Labs. Based on the model and a topological dual structure of Chua's chaotic circuit, a memristor-based fourth-order chaotic circuit was designed. As is verified by theoretical analysis, simulation and circuit realizations, the charge-control quadratic memristor-based chaotic circuit has complex dynamical behaviors relying on initial state of memristor. Meanwhile, non-linear dynamical phenomenon of state transition is generated along with variation of initial state, time and system parameters. An eye of scroll and an eye of limit cycle are observed in phase diagrams of chaotic circuits