Identifying and utilising various biomarkers for tracking Alzheimer's disease (AD) progression have received many recent attentions and enable helping clinicians make the prompt decisions. Traditional progression models focus on extracting morphological biomarkers in regions of interest (ROIs) from MRI/PET images, such as regional average cortical thickness and regional volume. They are effective but ignore the relationships between brain ROIs over time, which would lead to synergistic deterioration. For exploring the synergistic deteriorating relationship between these biomarkers, in this paper, we propose a novel spatio-temporal similarity measure based multi-task learning approach for effectively predicting AD progression and sensitively capturing the critical relationships between biomarkers. Specifically, we firstly define a temporal measure for estimating the magnitude and velocity of biomarker change over time, which indicate a changing trend(temporal). Converting this trend into the vector, we then compare this variability between biomarkers in a unified vector space(spatial). The experimental results show that compared with directly ROI based learning, our proposed method is more effective in predicting disease progression. Our method also enables performing longitudinal stability selection to identify the changing relationships between biomarkers, which play a key role in disease progression. We prove that the synergistic deteriorating biomarkers between cortical volumes or surface areas have a significant effect on the cognitive prediction.