Synthesis of a crosslinked polymer on single-walled carbon nanotubes (SWNTs) is a promising method for functionalization of the SWNTs due to their high coating stability together with their intactness to the SWNTs. We here reveal a requirement for vinyl monomers to form such crosslinked polymers on the SWNTs, which is highly important to generalize this method as well as to develop many polymer-SWNT hybrids with a unique structure and functions.