A fast implementation of the linear-prediction-based band selection (LPBS) method is proposed, and the method is denoted as fast-LPBS. The original LPBS method is an effective unsupervised band selection approach and can achieve satisfying classification performance in practice. It performs linear projections to measure the dissimilarity between spectral channels and adopts sequential forward search to avoid exhaustive search. However, LPBS is time-consuming because it involves a random initialization and much high-complexity calculation, such as high-order matrix multiplication, which limits its applications in many cases. The proposed fast-LPBS method derives the recursive formulae of linear prediction errors and achieves incremental calculation, which reduces the computational cost significantly. Moreover, a simplified initialization strategy is applied, which further reduces the computational complexity of fast-LPBS. Although the recursive formula and the simplified initialization strategy are used, these processes do not deteriorate the proposed method’s classification performance, in other words, fast-LPBS can yield almost the same results as LPBS in a much shorter time. Experimental results on simulated and real datasets verify that the proposed method can run fast and maintain the high classification performance as the original one.