In this paper, we propose a hyperspectral image anomaly detection model by the use of background joint sparse representation (BJSR). With a practical binary hypothesis test model, the proposed approach consists of the following steps. The adaptive orthogonal background complementary subspace is first estimated by the BJSR, which adaptively selects the most representative background bases for the local region. An unsupervised adaptive subspace detection method is then proposed to suppress the background and simultaneously highlight the anomaly component. The experimental results confirm that the proposed algorithm obtains a desirable detection performance and outperforms the classical RX-based anomaly detectors and the orthogonal subspace projection-based detectors.