In this study, a dendrimer-like polymer based on poly(ethylene oxide) (PEO) was synthesized through a combination of anionic ring-opening polymerization (AROP) and click reaction via arm-first method. Firstly, the polymeric arm, a linear PEO with one alkynyl group and two bromo groups, was synthesized by AROP of ethylene oxide followed by functionalization with propargyl bromide and esterified with 2-bromopropionic bromide. Second, a star PEO carrying three azide groups was synthesized though AROP of ethylene oxide used 1,1,1-tris(hydrosymethyl) ethane as initiator followed esterificated with 2-bromopropionic acid and azidation. By azide–alkyne click reactions between the azide-terminated PEO star polymer and linear PEO with functionalization alkynyl group, a three generation dendrimer-like PEO, G3-PEO-24Br, was successfully synthesized. The resulting polymers were observed to have precisely controlled molecular weights and compositions with narrow molecular weight distributions.