We developed a new method to covalently attach well-defined polymers onto carbon nanotubes (CNTs) using a radical reaction. Well-defined poly(t-butyl acrylate) [p(tBA)] was first prepared by atom transfer radical polymerization, which formed radicals at the end of the polymer chain through an atom transfer. The generated radicals at the chain ends added CNTs to generate covalently functionalized p(tBA)-grafted CNTs. The polymer-attached CNTs showed much improved solubility in organic solvents. The synthesized MWNT-g-p(tBA) and SWNT-g-p(tBA) were characterized by IR, TGA and Raman spectroscopy, clearly indicating the formation of covalent bonding between p(tBA) and CNTs.