Accurately predicting Alzheimer's disease (AD) progression is crucial for timely treatment and intervention before advanced stage of AD. In this paper, a method on AD prediction based on joint decision-making utilizing dual priority prediction hierarchical model is proposed, which converts the three category prediction problem on AD, mild cognitive impairment (MCI) and normal cognitive (NC) into two levels of two category prediction problem. Firstly, the statistical features are extracted from the time series data of magnetic resonance imaging (MRI) and cognitive scores (CSs), which is obtained from individual historical follow-up, and the high-importance MRI volume statistical features are selected using the weighted embedded feature selection method. Then, both the NC priority prediction hierarchical model and the AD priority prediction hierarchical model are constructed. Using the selected high-importance MRI volume statistical features and CSs statistical features, these two hierarchical models are used to achieve AD/MCI/NC three category prediction. The NC and AD individuals are first predicted, and finally the MCI individuals are determined. The proposed AD prediction method is evaluated on the TADPOLE dataset. The accuracy (ACC) and macro average of F_1 score of the proposed AD prediction method are 89.29% and 88.81%, respectively. The experimental results show that the proposed method is effective and better than conventional AD prediction method.