In recent years, researchers have found that palmprint is quite a promising biometric identifier as it has the merits of high distinctiveness, robustness, user friendliness, and cost effectiveness. Nearly all the existing palmprint recognition methods are based on one-to-one matching. However, recent studies have corroborated that matching based on image sets can usually lead to a better result. Consequently, in this paper, we present a novel approach for palmprint recognition based on image sets. In our approach, each gallery and query example contains a set of palmprint images captured from a same individual. Competitive code is used for palmprint feature extraction. After the feature extraction process, we use the method of sparse approximated nearest points (SANP) for palmprint image set classification. By calculating the minimum between-set distance, we can set the label of each testing palmprint set as that of the nearest training set. Effectiveness of the proposed approach has been corroborated by the experiments conducted on PolyU palmprint database.