In recent years, there has been increasing interest in the use of automatic computer-based systems for the detection of eye diseases including glaucoma. However, these systems are usually standalone software with basic functions only, limiting their usage in a large scale. In this paper, we introduce an online cloud-based system for automatic glaucoma screening through the use of medical image-based pattern classification technologies. It is designed in a hybrid cloud pattern to offer both accessibility and enhanced security. Raw data including patient's medical condition and fundus image, and resultant medical reports are collected and distributed through the public cloud tier. In the private cloud tier, automatic analysis and assessment of colour retinal fundus images are performed. The ubiquitous anywhere access nature of the system through the cloud platform facilitates a more efficient and cost-effective means of glaucoma screening, allowing the disease to be detected earlier and enabling early intervention for more efficient intervention and disease management.