Task-Oriented Semantic Communication (TOSC) has been regarded as a promising communication framework, serving for various Artificial Intelligence (AI) task driven applications. The existing TOSC frameworks focus on extracting the full semantic features of source data and learning low-dimensional channel inputs to transmit them within limited bandwidth resources. Although transmitting full semantic features can preserve the integrity of data meaning, this approach does not attain the performance threshold of the TOSC. In this paper, we propose a Task-oriented Adaptive Semantic Communication (TasCom) framework, which aims to effectively facilitate the execution of AI tasks by only sending task-related semantic features. In the TasCom framework, we first propose a Generative AI (GAI) architecture based Generative Joint Source-Channel Coding (G-JSCC) for efficient semantic transmission. Then, an Adaptive Coding Controller (ACC) is proposed to find the optimal coding scheme for the proposed G-JSCC, which allows the semantic features with significant contributions to the AI task to preferentially occupy limited bandwidth resources for wireless transmission. Furthermore, we propose a generative training algorithm to train the proposed TasCom for optimal performance. The simulation results show that the proposed TasCom outperforms the existing TOSC and traditional codec schemes on the object detection and instance segmentation tasks at all considered channel conditions.