Emulation of known neural behavior is difficult because of the highly complex. The Hodgkin-Huxley model that was developed by Alan Lloyd Hodgkin and Andrew Fielding Huxley explains how to the membrane potentials are conducted from one cell to another cell through the axon. Memristor have attracted great interest for various applications recently. The most interesting application of memristors is neural systems. In this paper, two different special memristor models based Hodgkin-Huxley (HH) circuit are presented. The memristor models are developed using TiO2 memristor mathematical model to emulate sodium and potassium channels and obtained voltage spikes train applying DC input current. Finally, the conductance characteristics of the developed special memristors are presented to obtain spikes train.