<p>A dual memristor four-dimensional hyperchaotic system with charge-controlled memristor and flux-controlled memristor is introduced in this paper. The basic dynamic properties analysize indicate that the system has infinitely line equilibrium points and rich memristor chaotic dynamics properties. The equivalent electronic circuit of the dual memristor hyperchaotic system is realized by means of integrated operational amplifiers and common electronic devices. The experimental results of the circuit are consistent with the numerical simulation results, which prove the existence and physical realizability of the system. Finally, a new image encryption algorithm is designed by combining the chaotic sequences generated by the new dual memristor hyperchaotic system with DNA dynamic encryption and image block diffusion. The initial values of the chaotic sequences are related to the pixel values of the original image, so it can effectively improve the resistance of encryption algorithms to plaintext attacks. The DNA matrix is divided into DNA sub-matrices blocks to realize diffusion operation, which greatly enhances the spatial complexity and security of the encryption algorithm. The simulation examples and algorithm security analysis demonstrate the effectiveness of the proposed encryption scheme.</p>