A hyperbranched-linear-hyperbranched (ABA) triblock copolymer containing poly(ethylene glycol) (PEG) as linear block and polyglycerol (hbPG) as hyperbranched blocks has been synthesized through a copper-catalysed click reaction. In order to synthesize the hyperbranched block, propargyl alcohol-initiated ring-opening multibranching polymerization of glycidol was used to prepare hbPG with the propargyl segment in the focal point (CH≡C-hbPG). Separately, PEG was functionalized at both ends using cyanuric chloride, and then the chloride groups of cyanuric chloride were substituted by azide groups. Finally, the azide-functionalized PEG was conjugated to CH≡C-hbPG via a click reaction. Substitution of the chlorine atoms of cyanuric chloride under different conditions together with click chemistry allows the synthesis of a variety of polymeric architectures. In the last step, fluorescein was attached to the block copolymer as a fluorescent probe in order to study the cell internalization of this copolymer. This type of triblock copolymer is a promising future nanomaterial for simultaneous drug delivery and cell imaging.