Abstract: A four-order charge-controlled memristor chaotic circuit is designed, and the dynamic equation of corresponding state variables is established.The stability of the equilibrium point is analyzed.The influence of initial conditions on the operating stateas well as the transient behavior under certain circuit parameters and initial conditions of the system is studied by combining bifurcation diagrams, Lyapunov exponent spectra, and phase trajectory diagrams.The block theory and DNA coding are applied to analyze the histogram, adjacent pixel correlation, key sensitivity, and information entropy of the image.The results indicate that changing the initial value of the internal state variables of the memristor can generate five different types of attractors, reflecting that the sensitivity of system dynamics to initial conditions; Under different circuit parameters and initial conditions, the system exhibits complex nonlinear dynamical behaviors such as transient chaos, intermittent chaos, and state transitions; The encryption algorithm based on the charge-controlled memristive chaotic system has high security, and the statistical performance analysis reflects the effectiveness of the image encryption algorithm, and shows the potential application of the algorithm in secure communication.