Memristor is introduced as the fourth basic circuit element. Memristor exhibits great potential for numerous applications, such as emulating synapse, while the mathematical model of the memristor is still an open subject. In the linear-drift model, the boundary condition of the device is not considered. This paper proposes an extended linear-drift model of the memristor. The extended linear-drift model keeps the linear characteristic and simplicity of the linear-drift model and considers the boundary condition of the device. A piecewise linear approximation model of the extended linear-drift model is given. Both models are suitable for describing the memristor.