Previous studies have developed fairness methods for biased models that exhibit discriminatory behaviors towards specific subgroups. While these models have shown promise in achieving fair predictions, recent research has identified their potential vulnerability to score-based membership inference attacks (MIAs). In these attacks, adversaries can infer whether a particular data sample was used during training by analyzing the model's prediction scores. However, our investigations reveal that these score-based MIAs are ineffective when targeting fairness-enhanced models in binary classifications. The attack models trained to launch the MIAs degrade into simplistic threshold models, resulting in lower attack performance. Meanwhile, we observe that fairness methods often lead to prediction performance degradation for the majority subgroups of the training data. This raises the barrier to successful attacks and widens the prediction gaps between member and non-member data. Building upon these insights, we propose an efficient MIA method against fairness-enhanced models based on fairness discrepancy results (FD-MIA). It leverages the difference in the predictions from both the original and fairness-enhanced models and exploits the observed prediction gaps as attack clues. We also explore potential strategies for mitigating privacy leakages. Extensive experiments validate our findings and demonstrate the efficacy of the proposed method.