Alzheimer’s disease poses a significant public health challenge in the global aging society. One of its main clinical symptoms is the gradual decline in cognitive abilities. A crucial topic in Alzheimer’s disease research is to establish models that link cognitive performance with neuroimaging data to identify neuroimaging biomarkers associated with cognitive abilities. However, neuroimaging data often exhibit high dimensions, heavy-tailed distributions, and outliers. These characteristics not only reduce the accuracy and stability of models but also pose challenges for result explanations. To address these issues, this study uses sparse quantile regression to model and perform feature selection on data from the Alzheimer’s disease neuroimaging initiative (ADNI). This study also explores the distribution characteristics of cognitive scores at different quantiles and identifies specific brain regions associated with cognitive abilities. Experimental results demonstrate that sparse quantile regression successfully identifies the brain regions relevant to cognitive abilities at different quantiles. This research shows the potential of applying sparse quantile regression in neuroimaging data analysis and provides a novel perspective and approach for neuroimaging research.