Autism spectrum disorder (ASD) is an age- and sex-related neurodevelopmental disorder that alters the brain's functional connectivity (FC). The changes caused by ASD are associated with different age- and sex-related patterns in neuroimaging data. However, most contemporary computer-assisted ASD diagnosis methods ignore the aforementioned age-/sex-related patterns. In this paper, we propose a novel sparse multiview task-centralized (Sparse-MVTC) ensemble classification method for image-based ASD diagnosis. Specifically, with the age and sex information of each subject, we formulate the classification as a multitask learning problem, where each task corresponds to learning upon a specific age/sex group. We also extract multiview features per subject to better reveal the FC changes. Then, in Sparse-MVTC learning, we select a certain central task and treat the rest as auxiliary tasks. By considering both task-task and view-view relationships between the central task and each auxiliary task, we can learn better upon the entire dataset. Finally, by selecting the central task, in turn, we are able to derive multiple classifiers for each task/group. An ensemble strategy is further adopted, such that the final diagnosis can be integrated for each subject. Our comprehensive experiments on the ABIDE database demonstrate that our proposed Sparse-MVTC ensemble learning can significantly outperform the state-of-the-art classification methods for ASD diagnosis.