This paper proposes a concise window function to build a memristor model, simulating the widely-observed non-linear dopant drift phenomenon of the memristor. Exploiting the non-linearity, the memristor model is applied to the in-situ neuromorphic solution for a cortex-inspired spiking neural network (SNN), spike-based Bayesian Confidence Propagation Neural Network (BCPNN). The improved memristor model utilizing the proposed window function is able to retain the boundary effect and resolve the boundary lock and inflexibility problem, while it is simple in form that can facilitate large-scale neuromorphic model simulation. Compared with the state-of-the-art general memristor model, the proposed memristor model can achieve a 5.8x reduction of simulation time at a competitive fitting level in cortex-comparable large-scale software simulation. The evaluation results show an explicit similarity between the non-linear dopant drift phenomenon of the memristor and the BCPNN learning rule, and the memristor model is able to emulate the key traces of BCPNN with a correlation coefficient over 0.99.