There exist two factors influencing the accuracy of conventional hyperspectral target detection. One is the inherent image noises induced by spectral distortion, and the other is the equal contributions of all adjacent pixels in the heterogeneous region. However, in fact the heterogeneity implies that the pixels are composed of different materials and possess different spectral characteristics. To address these problems, we propose a hyperspectral target detection method by the combination of spatially adaptive model and sparse representation. The noise sparse representation is utilized to reconstruct an accurate signal, in which the useful information in noises is extracted as possible to make the reconstructed signal be full of more features and be close to the original signal. In addition, a spatially adaptive weighted model is proposed to detect the similarity between central pixel and neighboring pixels, and to make full use of the relationship among neighboring pixels. The final experimental results show that the proposed method possesses a strong robustness compared with the conventional hyperspectral target detection methods.