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Accurate and reliable prediction of Alzheimer's disease (AD) progression is crucial for effective interventions and treatment to delay its onset. Recently, deep learning models for AD progression achieve excellent predictive accuracy. However, their predictions lack reliability due to the non-calibration defects, that affects their recognition and acceptance. To address this issue, this paper proposes a temporal attention-aware evidential recurrent network for trustworthy prediction of AD progression. Specifically, evidential recurrent network explicitly models uncertainty of the output and converts it into a reliability measure for trustworthy AD progression prediction. Furthermore, considering that the actual scenario of AD progression prediction frequently relies on historical longitudinal data, we introduce temporal attention into evidential recurrent network, which improves predictive performance. We demonstrate the proposed model on the TADPOLE dataset. For predictive performance, the proposed model achieves mAUC of 0.943 and BCA of 0.881, which is comparable to the SOTA model MinimalRNN. More importantly, the proposed model provides reliability measures of the predicted results through uncertainty estimation and the ECE of the method on the TADPOLE dataset is 0.101, which is much lower than the SOTA model at 0.147, indicating that the proposed model can provide important decision-making support for risk-sensitive prediction of AD progression. [ABSTRACT FROM AUTHOR]