Face presentation attack detection (PAD) plays a vital role in securing face recognition systems. While existing PAD methods have achieved strong detection performance, they often exhibit inconsistent behavior across demographic groups, raising concerns about fairness. To address this issue, we propose FairPAD, a novel framework that jointly improves PAD performance and demographic fairness. FairPAD consists of two core components: (1) an Adversarial Attribute Disentanglement module, which implicitly suppresses sensitive demographic information (e.g., gender, race) in the learned representations through adversarial supervision; and (2) a Demographic Distribution Alignment module, which encourages consistent feature representations across demographic groups by aligning latent distributions. To support fairness-aware evaluation and alleviate data imbalance, we construct a new PAD dataset by integrating our collected data with several publicly available datasets and enriching them with demographic attribute annotations. Extensive evaluations under both intra- and cross-dataset settings show that FairPAD consistently outperforms existing methods in both detection accuracy and fairness, demonstrating its potential for real-world deployment. Code and dataset are available at https://github.com/Wenjun216/FairPAD .