The recent large-scale text-to-image generative models have attained unprecedented performance, while people established adaptor modules like LoRA and DreamBooth to extend this performance to even more unseen concept tokens. However, we empirically find that this workflow often fails to accurately depict the out-of-distribution concepts. This failure is highly related to the low quality of training data. To resolve this, we present a framework called Controllable Adaptor Towards Out-of-Distribution Concepts (CATOD). Our framework follows the active learning paradigm which includes high-quality data accumulation and adaptor training, enabling a finer-grained enhancement of generative results. The aesthetics score and concept-matching score are two major factors that impact the quality of synthetic results. One key component of CATOD is the weighted scoring system that automatically balances between these two scores and we also offer comprehensive theoretical analysis for this point. Then, it determines how to select data and schedule the adaptor training based on this scoring system. The extensive results show that CATOD significantly outperforms the prior approaches with an 11.10 boost on the CLIP score and a 33.08% decrease on the CMMD metric.