This paper presents a memory crossbar based on two serial memristors with threshold characteristic to eliminate the effect of sneak paths, which is a key issue in crossbar memory system leading to great degradation in their performance and power efficiency. At first, we analyze the threshold characteristic of memristor and propose a memristor model with threshold. Based on this model, the paper presents the design and simulation of a non-volatile memory system utilizing two serial memristors with different polarities as a memory cell. This scheme solves the sneak-path problem by taking advantage of the threshold characteristic and the performance with having always high resistance state in all the memory cells, which is validated by simulation results. The scheme also possesses the superior properties of remarkable compatibility and high density.