Abstract: In recent years, significant progress has been made in the research of memristor synaptic-coupled neurons. However, most models only coupling the synapses and neurons and fail to incorporate the magnetic field effects generated by the charged ions around the neurons into the coupling. In this paper, a novel memristor model is presented, and in combination with the electromagnetic effect generated by ion exchange on the cell membrane, a memristor-coupled Fitz Hugh-Nagumo neuron chaotic model containing feedback terms is constructed. Theoretical analysis and numerical simulation show that the memristor-coupled neuron model can generate double scroll attractors under certain parameters. Then, the chaotic sequences generated by the proposed model and the DNA triploid mutation encoding are combined and applied in the image encryption algorithm. The experimental results show that the key space of this image encryption algorithm is 2266, the information entropy of the ciphertext is 7.9998, and the correlation of adjacent pixels is very close to 0, so the encryption algorithm has high security.