Human noroviruses (NoVs) are a major cause of gastroenteritis worldwide. It is thought that, similar to other RNA viruses, high mutation rates allow NoVs to evolve fast and to undergo rapid immune escape at the population level. However, the rate and spectrum of spontaneous mutations of human NoVs have not been quantified previously. Here, we analyzed the intra-patient diversity of the NoV capsid by carrying out RT-PCR and ultra-deep sequencing with 100,000-fold coverage of 16 stool samples from symptomatic patients. This revealed the presence of low-frequency sequences carrying large numbers of U-to-C or A-to-G base transitions, suggesting a role for hyper-mutation in NoV diversity. To more directly test for hyper-mutation, we performed transfection assays in which the production of mutations was restricted to a single cell infection cycle. This confirmed the presence of sequences with multiple U-to-C/A-to-G transitions, and suggested that hyper-mutation contributed a large fraction of the total NoV spontaneous mutation rate. The type of changes produced and their sequence context are compatible with ADAR-mediated editing of the viral RNA.