Existing Parkinson's disease (PD) speech recognition methods are predominantly based on fixed-text speech recognition and are specifically designed for a particular language, which limits their generalizability. To address this issue, this paper proposes a domain generalization method, termed Domain-Adversarial Representation Learning (DARL), for recognizing PD continuous speech. Specifically, DARL extracts domain-invariant features by jointly optimizing classification loss and distribution discrepancy loss, utilizing labeled fixed-text speech data and unlabeled target continuous speech data. By narrowing the domain gap between fixed-text and continuous speech data, the proposed approach significantly improves the model generalization capability across different languages. Experimental results on two tasks and multiple evaluation metrics consistently demonstrate the superior performance of the proposed method in PD continuous speech recognition.