Due to the successful development of deep image generation technology, forgery detection plays a more important role in social and economic security. Racial bias has not been explored thoroughly in the deep forgery detection field. In the paper, we first contribute a dedicated dataset called the Fair Forgery Detection (FairFD) dataset, where we prove the racial bias of public state-of-the-art (SOTA) methods. Different from existing forgery detection datasets, the self-construct FairFD dataset contains a balanced racial ratio and diverse forgery generation images with the largest-scale subjects. Additionally, we identify the problems with naive fairness metrics when benchmarking forgery detection models. To comprehensively evaluate fairness, we design novel metrics including Approach Averaged Metric and Utility Regularized Metric, which can avoid deceptive results. Extensive experiments conducted with nine representative forgery detection models demonstrate the value of the proposed dataset and the reasonability of the designed fairness metrics. We also conduct more in-depth analyses to offer more insights to inspire researchers in the community.