In a neuron model with adaptive feedback synapse, with the change of parameters, the existence of two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor,and then switching back to the two coexisting chaotic attractors in this model were recently reported. An electronic circuit design for this model is described in detail in this paper. The circuit design of the non-monotonous activation function unit is also considered in detail. The designed circuits are simulated using the Electronic Workbench (EWB) software. Simulation results demonstrate that the dynamical behaviors of the designed circuit are closely similar to those in numerical simulations.