In smart grid systems, security and privacy prevention is great concerns. The suppliers of the power in smart grid systems demand to know the consumption of each customer for correctly calculating billing price and the total amount of consumption in a certain region for managing energy supply adopted real-time needs. On the other hand, the customer of the power desires to hide his/her own consumption profile, since it contains privacy information of the customer. However, hiding the consumption allows customers to reduce billing price. Previous privacy-preserving smart metering schemes provide only one of billing or energy management functionality, or even if both of them are achieved, these schemes cannot verify the integrity of the consumption issued by the smart meter. We propose a novel smart metering scheme that provides both of billing and energy management functionality, as well as verifiability of the integrity of total amount of the consumption or billing price.