This paper presents a low power circuit design for an electronic nervous system composed of central pattern generator (CPG) to control a biomimetic robot that mimics the lamprey swimming system. The circuit has been designed using 65nm CMOS technology model at 0.8V supply. The design challenges of narrow voltage design margin and high sensitivity to parameter variation are addressed by circuit optimization techniques as well as amplitude and time parameter scaling. The electronic CPG consists of electronic neurons connected through electronic synapses, where the behaviors of the neuron and synapse adopt Hindmarsh-Rose (HR) dynamics to replicate biological neurons and a first order chemical synapse model is utilized to achieve active synapses. The simulation results validate the electronic CPG performance at 0.8V supply voltage with parameter variation tolerance of 5% dissipating 3.28mW. The die size of the chip is 1.1mm2 including I/O pads.