Due to the availability of only a few labeled instances for the novel target prediction task and the significant domain shift between the well annotated source domain and the target domain, cross-domain few-shot learning (CDFSL) induces a very challenging adaptation problem. In this paper, we propose a simple Adaptive Weighted Co-Learning (AWCoL) method to address the CDFSL challenge by adapting two independently trained source prototypical classification models to the target task in a weighted co-learning manner. The proposed method deploys a weighted moving average prediction strategy to generate probabilistic predictions from each model, and then conducts adaptive co-learning by jointly fine-tuning the two models in an alternating manner based on the pseudo-labels and instance weights produced from the predictions. Moreover, a negative pseudo-labeling regularizer is further deployed to improve the fine-tuning process by penalizing false predictions. Comprehensive experiments are conducted on multiple benchmark datasets and the empirical results demonstrate that the proposed method produces state-of-the-art CDFSL performance.