Facial recognition technology has been developed and widely used for decades. However, it has also made privacy concerns and researchers’ expectations for facial recognition privacy-preserving technologies. To provide privacy, detailed or semantic contents in face images should be obfuscated. However, face recognition algorithms have to be tailor-designed according to current obfuscation methods, as a result the face recognition service provider has to update its commercial off-the-shelf(COTS) products for each obfuscation method. Meanwhile, current obfuscation methods have no clearly quantified explanation. This paper presents a universal face obfuscation method for a family of face recognition algorithms using global or local structure of eigenvector space. By specific mathematical explanations, we show that the upper bound of the distance between the original and obfuscated face images is smaller than the given recognition threshold. Experiments show that the recognition degradation is 0% for global structure based and 0.3%-5.3% for local structure based, respectively. Meanwhile, we show that even if an attacker knows the whole obfuscation method, he/she has to enumerate all the possible roots of a polynomial with an obfuscation coefficient, which is computationally infeasible to reconstruct original faces. So our method shows a good performance in both privacy and recognition accuracy without modifying recognition algorithms.