We studied the molecular evolution of the capsid gene in all genotypes (genotypes 1–9) of human norovirus (NoV) genogroup I. The evolutionary time scale and rate were estimated by the Bayesian Markov chain Monte Carlo (MCMC) method. We also performed selective pressure analysis and B-cell linear epitope prediction in the deduced NoV GI capsid protein. Furthermore, we analysed the effective population size of the virus using Bayesian skyline plot (BSP) analysis. A phylogenetic tree by MCMC showed that NoV GI diverged from the common ancestor of NoV GII, GIII, and GIV approximately 2,800 years ago with rapid evolution (about 10−3 substitutions/site/year). Some positive selection sites and over 400 negative selection sites were estimated in the deduced capsid protein. Many epitopes were estimated in the deduced virus capsid proteins. An epitope of GI.1 may be associated with histo-blood group antigen binding sites (Ser377, Pro378, and Ser380). Moreover, BSP suggested that the adaptation of NoV GI strains to humans was affected by natural selection. The results suggested that NoV GI strains evolved rapidly and date back to many years ago. Additionally, the virus may have undergone locally affected natural selection in the host resulting in its adaptation to humans.