The excellent generalization, contextual learning, and emergence abilities in the pre-trained large models (PLMs) handle specific tasks without direct training data, making them the better foundation models in the adversarial domain adaptation (ADA) methods to transfer knowledge learned from the source domain to target domains. However, existing ADA methods fail to account for the confounder properly, which is the root cause of the source data distribution that differs from the target domains. This study proposes an adversarial domain adaptation with confounder balancing for PLMs fine-tuning (ADA-CBF). The ADA-CBF includes a PLM as the foundation model for a feature extractor, a domain classifier and a confounder classifier, and they are jointly trained with an adversarial loss. This loss is designed to improve the domain-invariant representation learning by diluting the discrimination in the domain classifier. At the same time, the adversarial loss also balances the confounder distribution among source and unmeasured domains in training. Compared to existing ADA methods, ADA-CBF can correctly identify confounders in domain-invariant features, thereby eliminating the confounder biases in the extracted features from PLMs. The confounder classifier in ADA-CBF is designed as a plug-and-play and can be applied in the confounder measurable, unmeasurable, or partially measurable environments. Empirical results on natural language processing and computer vision downstream tasks show that ADA-CBF outperforms the newest GPT-4, LLaMA2, ViT and ADA methods.