Target detection for Hyperspectral Images (HSIs) is gaining importance owing to its important military and civilian applications. This study proposed a novel target detection algorithm for HSIs based on tensor representation. The algorithm employed tensor analysis including CP and tensor block decompositions to implement blind source separation on hyperspectral data. First, effective spatial and spectral features of the blocks of local images were extracted. Then, a detection model based on sparse and collaborative representations was established. Experiments were conducted to evaluate the performance of our approach under multiple scenes with complex backgrounds. From the visual representation of the results, it can be concluded that the proposed approach effectively extracts the spatial-spectral features from scenes with strong noise and complex backgrounds. The approach has good ability to suppress the background and the target is salient. In addition, the performance of the approach is evaluated using quantitative metrics such as Receiver Operating Curve (ROC) and area under the ROC curve (AUC). Considering the popular HSI image of San Diego as an example, the approach achieves 90% detection rate with a false alarm rate of 10%, and the AUC is greater than 0.95. Hence, our approach outperforms other popular approaches.