Limited labeled training samples constitute a challenge in hyperspectral image classification, with much research devoted to cross-domain adaptation, where the classes of the source and target domains are different. Current cross-domain few-shot learning (FSL) methods only use a small number of sample pairs to learn the discriminant features, which limits their performance. To address this problem, we propose a new framework for cross-domain FSL, considering all possible positive and negative pairs in a training batch and not just pairs between the support and query sets. Furthermore, we propose a new kernel triplet loss to characterize complex nonlinear relationships between samples and design appropriate feature extraction and discriminant networks. Specifically, the source and target data are simultaneously fed into the same feature extraction network, and then, the proposed kernel triplet loss on the embedding feature and the cross-entropy loss on the softmax output are used to learn discriminant features for both source and target data. Finally, an iterative adversarial strategy is employed to mitigate domain shifts between source and target data. The proposed method significantly outperforms state-of-the-art methods in experiments on four target datasets and one source dataset. The code is available at https://github.com/kkcocoon/CFSL-KT.