In the case of hyperspectral anomaly detection, in order to make hyperspectral low-dimensional data preserve the spectral information more completely, a band selection method based on the optimal linear prediction of principal components in subspace was proposed. Hyperspectral bands are divided into different subspaces by spectral clustering with the improved correlation measure. The principal component analysis (PCA) of bands is presented in each subspace, and main components are selected as the reconstructed targets. The subspace tracking method serves as the search strategy, and several bands are selected from each subspace to perform the joint optimal linear prediction of reconstructed targets. The selected bands in each subspace are combined to obtain the optimal band subset. Experimental results show that, the proposed method can reconstruct the original data more completely. Compared with original data, and the band subsets obtained by adaptive band selection (ABS) method, linear prediction (LP) method, maximum-variance principal component analysis (MVPCA) method, auto correlation matrix-based band selection (ACMBS) method and optimal combination factors-based band selection (OCFBS) method, the band subset of proposed method has superior performance of anomaly detection.