With the rise of big data, cloud computing and the internet of things, terminal devices face great challenges in hardware and power. The demand of new high efficiency low power operation unit is becoming more and more urgent. A novel Booth multiplier with high efficiency and low power consumption was proposed to solve the problem of high power consumption of operational units. It could be used in image processing, multimedia processing, pattern recognition and other fault-tolerant applications. Experimental results showed that compared with the existing Booth multipliers, the proposed approximate Booth multiplier reduced the power consumption and delay by 19.3% and 28.6% respectively, and saved area by 29.0%. Meanwhile the approximate Booth multiplier also had some advantages in operation accuracy. Finally, the validity of the proposed approximate Booth multiplier was verified in the application of Gaussian filtering.