Min-Redundancy Max-Relevance (mRMR) is a feature selection methodology based on information theory. We explore the mRMR principle for automatic glaucoma diagnosis. Optimal candidate feature sets are acquired from a composition of clinical screening data and retinal fundus image data. An mRMR optimized classifier is further trained using the candidate feature sets to find the optimized classifier. We tested the proposed methodology on eye records of 650 subjects collected from Singapore Eye Research Institute. The experimental results demonstrate that the new classifier is much compact by using less than ¼ of the initial feature set. The ranked feature set also enables the clinicians to better access the diagnostic process of the algorithm. The work is a further step towards the advancement of the automatic glaucoma diagnosis.