Cardiac arrhythmia is known to be one of the most common causes of death worldwide. Therefore, development of efficient arrhythmia detection techniques is essential to save patients' lives. In this paper, we introduce a new real-time cardiac arrhythmia classification using memristor neuromorphic computing system for classification of 5 different beat types. Neuromorphic computing systems utilize new emerging devices, such as memristors, as a basic building block. Hence, these systems provide excellent trade-off between real-time processing, power consumption, and overall accuracy. Experimental results showed that the proposed system outperforms most of the methods in comparison in terms of accuracy and testing time, since it achieved 96.17% average accuracy and 34 ms average testing time per beat.