The transcranial sonography (TCS) based computer-aided diagnosis (CAD) for Parkinson's disease (PD) has attracted considerable attention. The learning using privileged information (LUPI) is a new learning paradigm, in which, the privileged information (PI) is only available for model training, but unavailable in the testing stage. The Random vector functional link network plus (RVFL+) algorithm is a newly proposed LUPI algorithm, which has shown its effectiveness for classification task. Moreover, the kernel-based RVFL+ (KRVFL+) has been proposed to overcome the randomness in RVFL+. In this work, we propose a cascaded KRVFL+ (cKRVFL+) algorithm for the single-modal TCS-based PD diagnosis. The predicted value of the former KRVFL+ classifier is adopted as the PI for the current KRVFL+, and only the KRVFL+ in the last layer is finally used as classifiers during the testing stage. This cascaded structure progressively promotes the discrimination performance of KRVFL+ classifier. The experimental results show the effectiveness of the cascaded LUPI classifier framework for single-modality TCS based diagnosis of PD, and the proposed cKRVFL+ algorithm achieves the best performance.