Abstract: Memristor is a new type of passive components, it has the characteristics of nanometer size, non-linearity and memory function.And it has been applied in model analysis, basic circuit design, electronic component design, integrated circuit design, synaptic and other aspects. In this paper, a hybrid CMOS memristor logic gate is designed, which uses an AND gate and OR gate based on memristor and an inverter based on CMOS process to realize an exclusive OR gate circuit based on memristor. Then, the two-bit Vedic multipliers are implemented using the memristor logic gate designed in this paper. The experimental results show that the two-bit Vedic multipliers designed in this paper compared with the existing two-bit Vedic multipliers, consumes approximately 80% of the original power and 76% of the area overhead when performing the same function.