We studied the nucleation mechanism of carbon nanotubes based on the hypothesis that the starting nanotube seed can be nucleated by rolling a small fragment of a graphite sheet (graphene) under thermal fluctuations. The energy barriers for rolling a graphene along different crystallographic directions are calculated from a tight-binding model,. We then estimate the relative weight of the large-amplitude fluctuations corresponding to low-frequency vibrational modes of graphene sheets of increasing size. Direct molecular dynamics simulation of the high- temperature fluctuation of a pair of parallel graphenes demonstrates that a nanotube closed at one end can spontaneously form. We discuss the combined effects due to: (a) the decrease of the energy barriers against rolling with increasing nanotube radius, and (b) the increase of random fluctuations with increasing size of the graphene sheet. The superposition of such effects may lead to a preferential range of nanotube diameters which could nucleate more abundantly than others.