Smart space has emerged as a new paradigm that combines sensing, communication, and artificial intelligence technologies to offer various customized services. A fundamental requirement of these services is person identification. Although a variety of person-identification approaches has been proposed, they suffer from several limitations in practical applications, such as low energy efficiency, accuracy degradation, and privacy issue. This article proposes an energy-harvesting-based privacy-preserving gait recognition scheme for smart space, which is named PrivGait. In PrivGait, we extract discriminative features from 1-D gait signal and design an attention-based long short-term memory (LSTM) network to classify different people. Moreover, we leverage a novel Bloom filter-based privacy-preserving technique to address the privacy leakage problem. To demonstrate the feasibility of PrivGait, we design a proof-of-concept prototype using off-the-shelf energy-harvesting hardware. Extensive evaluation results show that the proposed scheme outperforms state of the art by 6%-10% and incurs low system cost while preserving user's privacy.