The detection of electricity theft, which focuses on privacy protection and system security, has been extensively researched in the smart grid. However, existing solutions have not taken into account the enormous communication overhead that will be incurred in practical environments due to the large scale of the smart grid and the vast number of smart meters. Furthermore, there has been a lack of further research on the detection models and periods. Therefore, we propose a lightweight privacy-preserving electricity theft detection scheme. Specifically, we introduce differential privacy in the inner product encryption process of electricity data and neural network weights under the vector type, providing strict privacy protection without affecting data utility. Secondly, a combination detection model that extracts local and global features of electricity data is proposed. Furthermore, we explore the impact of detection periods on six different datasets. The experimental results based on real electricity consumption data demonstrate that our scheme has lower communication overhead and higher accuracy.