Existing work on fairness modeling commonly assumes that sensitive attributes for all instances are fully available, which may not be true in many real-world applications due to the high cost of acquiring sensitive information. When sensitive attributes are not disclosed or available, it is needed to manually annotate a small part of the training data to mitigate bias. However, the skewed distribution across different sensitive groups preserves the skewness of the original dataset in the annotated subset, which leads to non-optimal bias mitigation. To tackle this challenge, we propose Active Penalization Of Discrimination (APOD), an interactive framework to guide the limited annotations towards maximally eliminating the effect of algorithmic bias. The proposed APOD integrates discrimination penalization with active instance selection to efficiently utilize the limited annotation budget, and it is theoretically proved to be capable of bounding the algorithmic bias. According to the evaluation on five benchmark datasets, APOD outperforms the state-of-the-arts baseline methods under the limited annotation budget, and shows comparable performance to fully annotated bias mitigation, which demonstrates that APOD could benefit real-world applications when sensitive information is limited. The source code of the proposed method is available at: https://github.com/guanchuwang/APOD-fairness.