In this paper, high order sliding mode control is proposed to realize the synchronization of two Ghostburster neurons under external electrical stimulation. Being a motion on a discontinuity set of a dynamic system, the sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. As the high order sliding mode technique employed in this paper, it considers a fractional power of the absolute value of the tracking error coupled with the sign function. This structure provides several advantages such as the simplification of the control law, higher accuracy and chattering prevention. Firstly we analyze the periodic and chaotic dynamics of individual Ghostburster neuron under different external electrical stimulus, then high order sliding mode controller is designed to synchronize two Ghostburster neurons and drive the slave neuron to act as the master one. Asymptotic synchronization of the system can be obtained by proper choice of the control parameters. Simulation results demonstrate the effectiveness of the proposed control method.