The smart grid is an evolving critical infrastructure, which combines renewable energy and the most advanced information and communication technologies to provide more economic and secure power supply services. To cope with the intermittency of ever-increasing renewable energy and ensure the security of the smart grid, state estimation, which serves as a basic tool for understanding the true states of a smart grid, should be performed with high frequency. More complete system state data are needed to support high-frequency state estimation. The data completeness problem for smart grid state estimation is therefore studied in this paper. The problem of improving data completeness by recovering high-frequency data from low-frequency data is formulated as a super resolution perception (SRP) problem in this paper. A novel machine-learning-based SRP approach is thereafter proposed. The proposed method, namely the Super Resolution Perception Net for State Estimation (SRPNSE), consists of three steps: feature extraction, information completion, and data reconstruction. Case studies have demonstrated the effectiveness and value of the proposed SRPNSE approach in recovering high-frequency data from low-frequency data for the state estimation.