Hyperspectral target detection is crucial in Earth observation for both military and civilian applications. However, complex backgrounds and the scarcity of target samples pose challenges in hyperspectral image analysis. In this paper, we first employ the CEM coarse detection method to extract background data. Subsequently, a novel knowledge distillation model, namely KDTGAN (implemented through Transformer-GAN), is introduced. The generator of this teacher model adopts the structure of a Transformer encoder and combines it with a multi-scale data fusion approach to accurately learn the background distribution, which in turn enables target detection by reconstructing the background information. To overcome the challenge of unstable GAN training, especially the scarcity of pure background data, we propose a new loss algorithm to reduce the negative impact of suspicious target samples on model performance. To reduce the computational burden of the model, we introduce knowledge distillation and design a new distillation loss to constrain the student model to lighten the model while improving the student model's detection accuracy. The experimental results show that KDTGAN performs better than current detection methods with higher detection accuracy and robustness.