According to the fact that the basic features of a palmprint, including principal lines, wrinkles and ridges,have different resolutions, in this paper we analyze palmprints using a multi-resolution method and define a novel palmprint feature, which called wavelet energy feature (WEF), based on the wavelet transform. WEF can reflect the wavelet energy distribution of the principal lines, wrinkles and ridges in different directions at different resolutions (scales), thus it can efficiently characterize palmprints. This paper also analyses the discriminabilities of each level WEF and, according to these discriminabilities, chooses a suitable weight for each level to compute the weighted city block distance for recognition. The experimental results show that the order of the discriminabilities of each level WEF, from strong to weak, is the 4th, 3rd,5th, 2nd and 1st level. It also shows that WEF is robust to some extent in rotation and translation of the images. Accuracies of 99.24% and 99.45% have been obtained in palmprint verification and palmprint identification, respectively. These results demonstrate the power of the proposed approach.