Objective: Alzheimer's disease (AD) is a slowly progressive neurodegenerative disorder with insidious onset. Accurate prediction of the disease progression has received increasing attention. Cognitive scores that reflect patients' cognitive status have become important criteria for predicting AD. Most existing methods consider the relationship between neuroimages and cognitive scores to improve prediction results. However, the inherent structure information in interrelated cognitive scores is rarely considered. Method: In this article, we propose a relation-aware tensor completion multitask learning method (RATC-MTL), in which the cognitive scores are represented as a third-order tensor to preserve the global structure information in clinical scores. We combine both tensor completion and linear regression into a unified framework, which allows us to capture both inter and intra modes correlations in cognitive tensor with a low-rank constraint, as well as incorporate the relationship between biological features and cognitive status by imposing a regression model on multiple cognitive scores. Result: Compared to the single-task and state-of-the-art multi-task algorithms, our proposed method obtains the best results for predicting cognitive scores in terms of four commonly used metrics. Furthermore, the overall performance of our method in classifying AD progress is also the best. Conclusion: Our results demonstrate the effectiveness of the proposed framework in fully exploring the global structure information in cognitive scores. Significance: This study introduces a novel concept of leveraging tensor completion to assist in disease diagnoses, potentially offering a solution to the issue of data scarcity encountered in prolonged monitoring scenarios.