The main purpose of this research is to develop a visual programming game with a Qualifying Rank strategy (QRVPG), allowing learners to use this system to conduct a STEAM-oriented mathematics course, the content of which is permutation. In the QRVPG system, learners can perform learning tasks with lower cognitive levels in their personal game copies to understand and construct knowledge, as the level of the game role increases, levels with higher cognitive levels will also appear. Then, learners are necessary to analyze and apply the knowledge they learned to complete more difficult learning tasks. In addition, learners can compete in the QRVPG system. This research hopes to introduce the qualifying rank strategy to allow learners with similar abilities to compete with each other, through this way, enhance learners’ learning motivation and engagement. In general, this research hopes to improve learners’ core competence in all aspects of STEAM through the cooperation of game formation and the gradual development of cognitive level.