Electrocardiography (ECG) is a non-invasive tool for predicting cardiovascular diseases (CVDs). Current ECG-based diagnosis systems show promising performance owing to the rapid development of deep learning techniques. However, the label scarcity problem, the co-occurrence of multiple CVDs and the poor performance on unseen datasets greatly hinder the widespread application of deep learning-based models. Addressing them in a unified framework remains a significant challenge. To this end, we propose a multi-label semi-supervised model (ECGMatch) to recognize multiple CVDs simultaneously with limited supervision. In the ECGMatch, an ECGAugment module is developed for weak and strong ECG data augmentation, which generates diverse samples for model training. Subsequently, a hyperparameter-efficient framework with neighbor agreement modeling and knowledge distillation is designed for pseudo-label generation and refinement, which mitigates the label scarcity problem. Finally, a label correlation alignment module is proposed to capture the co-occurrence information of different CVDs within labeled samples and propagate this information to unlabeled samples. Extensive experiments on four datasets and three protocols demonstrate the effectiveness and stability of the proposed model, especially on unseen datasets. As such, this model can pave the way for diagnostic systems that achieve robust performance on multi-label CVDs prediction with limited supervision.