Early detection of children with autism spectrum disorder (ASD) has been of great interest to researchers due to an increase in the rate of autism incidence around the world. However, a diagnosis of ASD is still challenging to receive in a timely manner for the large-scale population because the current diagnostic practice requires considerable cost and time, and do not provide quantitative feedback. In this paper, we explore a new ASD screening method, namely Gaze-Wasserstein, that is non-invasive, fast, and widely accessible. Based on the gaze tracking and analysis, Gaze-Wasserstein is able to provide objective gaze pattern-based measurements for home-based ASD screening, and can eventually be deployed on any mobile technologies with a front camera. To test the performance of Gaze-Wasserstein, we conducted a pilot study with 32 child participants where 16 children have ASD and 16 children are typically developing. Evaluation results demonstrate the effectiveness and time-efficiency of our proposed method in the ASD screening, which indicate that our Gaze-Wasserstein is a promising autism screening approach in the clinical practice.