While the number of children with diagnosed autism spectrum disorder (ASD) continues to rise from year to year, there is still no universal approach to autism diagnosis and treatment. A great variety of different tools and approaches for the on-site diagnostic are available right now, however, a big percent of parents have no access to them and they tend to search for the available tools and correction programs on the Internet. Lack of money, absence of qualified specialists, and low level of trust to the correction methods are the main issues that affect the in-time diagnoses of ASD and which need to be solved to get the early treatment for the little patients. Understanding the importance of this issue our team decided to investigate new methods of the online autism diagnoses and develop the algorithm that will be able to predict the chances of ASD according to the information from the gaze activity of the child. The results that we got during the experiments show supported our idea that eye-tracking technology is one of the most promising tools for the early detection of the eye-movement features that can be markers of the ASD. Moreover, we have conducted a series of experiments to ensure that our approach has a reliable result on the cheap webcam systems. Thus, this approach can be used as an additional first screening tool for the home monitoring of the early child development and ASD connected disorders monitoring. The further development of eye-tracking based autism diagnosis has a big potential of usage and can be further implemented in the daily practice for practical specialists and parents.