Movement pattern mining is a key focus in movement data research, with moving flock patterns holding particular significance due to their potential to reveal valuable insights across various domains. This research aimed to discover moving flock patterns in movement data. To achieve this, we first developed a more precise definition of a moving flock by refining the existing definitions. Then, we proposed a taxonomy of flock patterns, enabling the derivation of distinct types of moving flock patterns. Finally, we developed a Reeb graph-based approach to discover desired moving flock patterns. The effectiveness of the approach was validated using movement data obtained from a real football match. In the results, 72 and 94 moving flock patterns were discovered under different cases, respectively. Moreover, the proportion of desired moving flock patterns in these cases was 29.17% and 24.47%, respectively. The results show that the proposed approach effectively detects the desired moving flock patterns, and the findings provide insightful information to sports professionals.