There are always high false alarm ratios when warning against the severe hail with the severe hail index (SHI) which is supplied by digital weather radar system. To solve this problem, the extraction algorithm with several novel features, such as "overhang", is designed and realized, and these features can describe the severe hail conceptual model from different aspects. Then we take short-time heavy rainfall cells which are easy to be confused with severe hail cells as counter examples to perform statistic analysis for these features and the SHI. Test results show that they have more significant difference between two kinds of samples and hence each of them can reflect one aspect characteristic of severe hail cells. Then a severe hail recognition model that is the Support Vector Machine with radial primary kernel function is learned. Finally, the normalized distance between the sample to be recognized and the optimal separating hyper-plane is determined as a new SHI for warning against the severe hail. Experimental results show that the method proposed in this paper makes severe hail hit ratio higher than the SHI being used and the false alarm ratio is reduced substantially.