The memristor is a nanostructure resistive tuning two terminal novel electronics device that has been widely explored in the area of neuromorphic computing systems, memories, digital circuits, analog circuits and many more new applications. In this article an efficient and flexible window function is presented for linear drift memristor model. Propose window function provides a unique feature (controllable window function discontinuity) to linear drift memristor model by which DPHL (Distorted Pinched Hysteresis Loop) problem is resolved and also improved the programming resistance state of the memristor. Five control parameters are introduced in the presented window function, in order to fix the pre-existing problem (like boundary effect, boundary lock and inflexibility) and make it more flexible. The programmable analog gain amplifier circuit is ultimately executed to instantiate the utilization of evolved memristor model.