Hyperspectral image (HSI) exhibits high-quality spectral signals that convey subtle differences, enabling the discrimination of similar materials and providing a unique advantage for anomaly detection (AD). Fine spectral of anomalies can be effectively identified amidst heterogeneous background pixels. Given the similarity of materials in spatial and spectral dimensions, joint utilization of spatial and spectral information enhances detection performance. However, many existing AD approaches for HSIs usually achieve high accuracy at the expense of high computational complexity. In response to the requirements of practical detection scenarios-efficiency, robustness, and accuracy-this article introduces a rapid and robust AD algorithm through discriminative band selection for HSIs. We propose a spatial-spectral feature extraction strategy to ensure detection accuracy. Initially, to effectively mine context information across a broad spectral range, the HSI cube in space is partitioned into several groups using a coarse-to-fine strategy. Subsequently, we identify the most relevant and informative bands based on spatial local density and spectral information entropy, forming the coarse HSI bands subset. Following this, we design a multiband target-background ratio (MBTBR) to capture strongly discriminative bands, resulting in the fine HSI bands subset. Finally, we present an adaptively spatial-spectral feature extraction strategy to detect anomalous targets. Extensive experimental results on real hyperspectral datasets demonstrate that the proposed method achieves satisfactory performance compared to the state-of-the-art algorithms, validating its strong robustness and low computational complexity simultaneously.