There have been growing concerns regarding the out-of-domain generalization ability of natural language processing (NLP) models, particularly in question-answering (QA) tasks. Current synthesized data augmentation methods for QA are hampered by increased training costs. To address this issue, we propose a novel approach that combines prompting methods and linear probing with fine-tuning strategy, which does not entail additional cost. Our method has been theoretically and empirically shown to be effective in enhancing the generalization ability of both generative and discriminative models. Our approach outperforms state-of-the-art baselines, with an average increase in F1 score of 4.5%-7.9%. Furthermore, our method can be easily integrated into any pre-trained models and offers a promising solution to the under-explored cross-domain QA task.