This paper presents a novel method for quantitative and objective diagnoses of Autism Spectrum Disorder (ASD) using eye tracking and deep neural networks. ASD is prevalent, with 1.5% of people in the US. The lack of clinical resources for early diagnoses has been a long-lasting issue. This work differentiates itself with three unique features: first, the proposed approach is data-driven and free of assumptions, important for new discoveries in understanding ASD as well as other neurodevelopmental disorders. Second, we concentrate our analyses on the differences in eye movement patterns between healthy people and those with ASD. An image selection method based on Fisher scores allows feature learning with the most discriminative contents, leading to efficient and accurate diagnoses. Third, we leverage the recent advances in deep neural networks for both prediction and visualization. Experimental results show the superior performance of our method in terms of multiple evaluation metrics used in diagnostic tests.