High oleic acid peanuts have higher oleic acid content and stronger oxidation stability than common peanuts, but their appearances are similar, which imposes difficulties for classifying. Based on this, the study aims to classify high oleic acid peanut to ensure its purity by using hyperspectral imaging technology. However, classification accuracy and efficiency are limited given the large amount of redundant information of hyperspectral images. The band iteration algorithm (BIA) is proposed to select characteristic bands by reducing the redundant information between spectral bands for the peanut classification. Hyperspectral images with 616 bands (from 400 nm to 1100 nm) of 126 high oleic acid peanuts and 126 common peanuts were collected. Then, BIA selected optimal bands as characteristic bands from adjacent bands according to the classification accuracy of each band subsets. Thirdly, three classification models, namely linear discriminant analysis, support vector machine, and partial least squares-discriminant analysis (PLS-DA), were employed to compare the performance of BIA with successive projections algorithm and competitive adaptive reweighted sampling, respectively. The experimental results show that BIA can effectively improve the classification ability of spectral data. The BIA-PLS-DA model had the best classification efficiency, and the accuracy of the test set reached 93.26%. For peanut individuals, only one peanut sample was misclassified with a classification error rate of 1.43%.