It is challenging to derive early diagnosis from neuroimaging data for autism spectrum disorder (ASD). In this work, we propose a novel sparse multi-view task-centralized (Sparse-MVTC) classification method for computer-assisted diagnosis of ASD. In particular, since ASD is known to be age- and sex-related, we partition all subjects into different groups of age/sex, each of which can be treated as a classification task to learn. Meanwhile, we extract multi-view features from functional magnetic resonance imaging to describe the brain connectivity of each subject. This formulates a multi-view multi-task sparse learning problem and it is solved by a novel Sparse-MVTC method. Specifically, we treat each task as a central task and other tasks as the auxiliary ones. We then consider the task-task and view-view relations between the central task and each auxiliary task. We can use this task-centralized strategy for a highly efficient solution. The comprehensive experiments on the ABIDE database demonstrate that our proposed Sparse-MVTC method can significantly outperform the existing classification methods in ASD diagnosis.