In power utility service outsourcing, some time-sensitive computations (e.g., dynamic prices prediction) are outsourced to a third-party service provider. This brings in new privacy threats to customers. Although some existing works focus on achieving privacy-preserving temporal and spatial aggregation for one center, they basically cannot be directly applied to the scenario of service outsourcing with multiple centers (e.g., with power utility and service providers). We thus propose a privacy-preserving service outsourcing scheme, called PPSO, for real-time pricing demand response in smart grid with fault tolerance and flexible customers' enrollment and revocation. In our proposed PPSO, power utility can outsource the dynamic pricing prediction to a service provider, while still preserving customers' privacy. Extensive experiment results demonstrate that PPSO has less computation overhead and lower transmission delay compared with existing schemes.