Training with diverse teammates is the key for learning generalizable agents. Typical approaches aim to generate diverse teammates by utilizing techniques like randomization, designing regularization terms, or reducing policy compatibility, etc. However, such teammates lack semantic information, resulting in inefficient teammate generation and poor adaptability of the agents. To tackle these challenges, we propose Semantically Diverse Teammate Generation (SemDiv), a novel framework leveraging the capabilities of large language models (LLMs) to discover and learn diverse coordination behaviors at the semantic level. In each iteration, SemDiv first generates a novel coordination behavior described in natural language, then translates it into a reward function to train a teammate policy. Once the policy is verified to be meaningful, novel, and aligned with the behavior, the agents train a policy for coordination. Through this iterative process, SemDiv efficiently generates a diverse set of semantically grounded teammates, enabling agents to develop specialized policies, and select the most suitable ones through language-based reasoning to adapt to unseen teammates. Experiments show that SemDiv generates teammates covering a wide range of coordination behaviors, including those unreachable by baseline methods. Evaluation across four MARL environments, each with five unseen representative teammates, demonstrates SemDiv’s superior coordination and adaptability. Our code is available at https://github.com/lilh76/SemDiv.