Polycaprolactone (PCL) was covalently grafted on the surface of carbon nanotubes by a simple click reaction of propargyl-terminated PCL (propargyl-PCL) and carbon nanotubes (CNTs) containing azide groups (MWNT-N-3). Propargyl-PCL was synthesized by the ring-opening polymerization of epsilon-caprolactone using propargyl alcohol and stannous octoate. MWNT-N-3 was prepared from MWNT having 2-bromoisobutyryl groups (MWNT-Br) with sodium azide by azidation. The melting temperature of propargyl-PCL was shifted to the high temperature in PCL-grafted MWNT. The thermal stability of PCL-grafted MWNT was enhanced as compared to that of propargyl-PCL. PCL was coated on the surface of MWNT with a high density of PCL chains, which showed good solubility of PCL-grafted MWNT in organic solvents. PCL-grafted MWNT was characterized with FT-IR, H-1 NMR, Raman, differential scanning calorimetry, thermogravimetric analysis, and scanning electron microscopy.