Influenced by the dynamic changes in the severity of illness, patients usually take examinations in hospitals irregularly, producing a large volume of irregular medical time-series data. Performing diagnosis prediction from the irregular medical time series is challenging because the intervals between consecutive records significantly vary along time. Existing methods often handle this problem by generating regular time series from the irregular medical records without considering the uncertainty in the generated data, induced by the varying intervals. Thus, a novel Uncertainty-Aware Convolutional Recurrent Neural Network (UA-CRNN) is proposed in this article, which introduces the uncertainty information in the generated data to boost the risk prediction. To tackle the complex medical time series with subseries of different frequencies, the uncertainty information is further incorporated into the subseries level rather than the whole sequence to seamlessly adjust different time intervals. Specifically, a hierarchical uncertainty-aware decomposition layer (UADL) is designed to adaptively decompose time series into different subseries and assign them proper weights in accordance with their reliabilities. Meanwhile, an Explainable UA-CRNN (eUA-CRNN) is proposed to exploit filters with different passbands to ensure the unity of components in each subseries and the diversity of components in different subseries. Furthermore, eUA-CRNN incorporates with an uncertainty-aware attention module to learn attention weights from the uncertainty information, providing the explainable prediction results. The extensive experimental results on three real-world medical data sets illustrate the superiority of the proposed method compared with the state-of-the-art methods.