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Cumulative studies have revealed that RNA N6-methyladenosine (m6A) modification plays a critical role in various human complex diseases including cancers. Exploring the relationship between m6As and diseases can reveal the molecular mechanism of disease pathogenesis. However, the known associations between m6As and diseases are very rare due to the time-consuming and laborious biological experiments. Some computational approaches have been proposed to predict the potential m6A-disease associations. However, these methods are restricted to specific application scenarios. To solve this limitation, we propose a novel computational framework, named m6A-Disease Prediction using Graph Convolutional Networks and Positive-Unlabeled Learning with Self-Adaptive Sampling (m6ADP-GCNPUAS), to accurately predict m6A-disease associations. m6ADP-GCNPUAS effectively captures the embedded features of m6A sites or diseases using GCN. Given the very limited m6A-disease associations, m6ADP-GCNPUAS adopts the PUAS framework to augment the potential positive samples, which improves the predictive power for m6A-disease associations. The experimental results indicate that m6ADP-GCNPUAS achieves over 0.99 across six evaluation metrics and PUAS significantly improves the predicted performance. In addition, case studies demonstrate that the predicted cancer-associated m6A sites participate in the regulation of cancer development and some predicted m6A genes could be the hallmarks for different cancers.