The fourth fundamental circuit element memristor completes the missing link between charge and magnetic flux. It consists of the function of the resistor as well as memory in nonlinear fashion. The property of the memristor depends on the magnitude and direction of applied potential. This unique property makes it the primitive building block for many applications such as resistive memories, soft computing, neuromorphic systems and chaotic circuits etc. In this paper we report TiO2-based nanostructured memristor modelling. The present memristor model is constructed in MATLAB environment with consideration of the linear drift model of memristor. The result obtained from the linear drift model is well matched with earlier reported results by other research groups. The fourth fundamental circuit element memristor completes the missing link between charge and magnetic flux. It consists of the function of the resistor as well as memory in nonlinear fashion. The property of the memristor depends on the magnitude and direction of applied potential. This unique property makes it the primitive building block for many applications such as resistive memories, soft computing, neuromorphic systems and chaotic circuits etc. In this paper we report TiO2-based nanostructured memristor modeling. The present memristor model is constructed in MATLAB environment with consideration of the linear drift model of memristor. The result obtained from the linear drift model is well matched with earlier reported results by other research groups.