Face restoration (FR) recovers high resolution (HR) faces from low resolution (LR) faces and is challenging due to its ill-posed nature. With years of development, existing methods can produce quality HR faces with realistic details. However, we observe that key facial attributes (e.g., age and gender) of the restored faces could be dramatically different from the LR faces and call this phenomenon attribute bias, which is fatal when using FR for applications such as surveillance and security. Thus, we argue that FR should consider not only image quality as in existing works but also attribute bias. To this end, we thoroughly analyze attribute bias with extensive experiments and find that two major causes are the lack of attribute information in LR faces and bias in the training data. Moreover, we propose the DebiasFR framework to produce HR faces with high image quality and accurate facial attributes. The key design is to explicitly model the facial attributes, which also allows to adjust facial attributes for the output HR faces. Experiment results show that DebiasFR has comparable image quality but significantly smaller attribute bias when compared with state-of-the-art FR methods.