The tremendous progress in deep learning has enabled to extract soft-biometric attributes from faces, which raises privacy concerns over images collected for face recognition. Advances toward attribute privacy have been able to conceal multiple attributes while preserving identity information but suffer from limitations: they 1) only consider a few soft-biometric attributes and 2) fail to support reversibility for attribute privacy preservation. To break these limitations, we design a reversible privacy-preserving scheme for various face attributes, called reversible attribute privacy preservation (RAPP). RAPP benefits from two modules: 1) The attribute obfuscator introduces a stream cipher to determine that special attributes have to be concealed with the user-defined password, which also supports recovering original attributes. 2) The attribute adversarial network is proposed to generate perturbed images that conceal various attributes while retaining the utility of face verification. In addition, when a wrong password is provided, the returned image with wrong attribute classification results still keeps realistic, which confuses an attacker to know whether the recovery is correct. Extensive experiments demonstrate that RAPP enables to conceal various attributes and recover original images while facilitating face verification.