Functional hyperbranched polyglycerols (PGs) have recently garnered considerable interest due to their potential in biomedical applications. Here, we present a one-pot synthesis of hyperbranched PGs possessing amine functionality using a novel amino glycidyl ether monomer. A Boc-protected butanolamine glycidyl ether (BBAG) monomer was designed and polymerized with glycidol (G) through anionic ring-opening multibranching polymerization to yield a series of hyperbranched P(G-co-BBAG) with controlled molecular weights (4800-16700 g/mol) and relatively low molecular weight distributions (1.2-1.6). The copolymerization and subsequent deprotection chemistry allow the incorporation of an adjustable fraction of primary amine moieties (typically, 5-20% monomer ratio) within the hyperbranched PG backbones, thus providing potentials for varying charge densities and functionality in PGs. The copolymerization kinetics of G and BBAG was also evaluated using a quantitative in situ 13C NMR spectroscopic analysis, which revealed gradient copolymerization between the comonomers. The free amine groups within the deprotected P(G-co-BAG) copolymer were further utilized for a facile conjugation chemistry with a model molecule in a quantitative manner. Furthermore, the superior biocompatibility of the prepared P(G-co-BAG) polymers was demonstrated via cell viability assays, outperforming many existing polyamines possessing relatively high cytotoxicity. Taken together, the biocompatibility with facile conjugation chemistry of free amine groups sheathed within the framework of hyperbranched PGs holds the prospect of advancing biological and biomedical applications.