Based on the improved electromagnetic induction neuron model, the coherent resonance (CR) phenomenon of the Memristor Hindmarsh-Rose (HR) network is studied. In addition to electrical coupling connecting gaps between adjacent neurons, magnetic coupling is used to describe the effect of field coupling between neurons. The dynamic analysis of the stable point is performed using the bifurcation diagram and phase diagram, and the potential dynamic mechanism of the emergence of CR and the change of discharge mode are explained. It is found that white Gaussian noise can induce CR in the resting state near the subcritical Hopf bifurcation of memristor neurons, and the occurrence of CR is related to the change of firing mode caused by the increase of noise amplitude.