Two amphiphilic block copolymers using hydrophobic poly(e-caprolactone) (PCL) and hydrophilic poly(ethylene glycol) (PEG) were successfully synthesized. One of them is an (A-b-B)(4) type star polymer [(PCL-b-PEG)(4)] and the other one is a Y-shaped PEG-(PCL)(2). A star-shaped polymer (PCL-b-PEG)(4) was prepared by ring-opening polymerization (ROP) of epsilon-caprolactone continued by click reaction of (PCL-azide)(4) and PEG-alkyne. The synthesis of Y-shaped PEG-(PCL)(2) block copolymer was carried out via Diels-Alder click reaction of a furan protected maleimide end-functionalized PEG (PEG-MI) with an anthracene end-functionalized PCL following the ROP of epsilon-caprolactone. The characterization of micelles is carried out using both materials in aqueous media as drug delivery vehicles, which showed satisfying results and enhanced the cytotoxic effect of the anti-cancer drug vinorelbine (VLB). However, micelles consisted of Y-shaped unimers were found to be more convenient for delivery of hydrophobic drugs such as VLB because they formed in lower concentration, carrying a higher amount of drugs and owing a monomodal distribution. We concluded that the free tails of hydrophobic chains in Y-shaped block copolymer facilitate the assembly of amphiphilic material in water to form micelles.