Face recognition is an effective technology for identifying a target person by facial images. However, sensitive facial images raises privacy concerns. Although privacy-preserving face recognition is one of potential solutions, this solution neither fully addresses the privacy concerns nor is efficient enough. To this end, we propose an efficient privacy-preserving solution for face recognition, named Pura, which sufficiently protects facial privacy and supports face recognition over encrypted data efficiently. Specifically, we propose a privacy-preserving and non-interactive architecture for face recognition through the threshold Paillier cryptosystem. Additionally, we carefully design a suite of underlying secure computing protocols to enable efficient operations of face recognition over encrypted data directly. Furthermore, we introduce a parallel computing mechanism to enhance the performance of the proposed secure computing protocols. Privacy analysis demonstrates that Pura fully safeguards personal facial privacy. Experimental evaluations demonstrate that Pura achieves recognition speeds up to 16 times faster than the state-of-the-art.