Polymers bearing pendant carbohydrates have a variety of biomedical applications especially in the area of targeted drug delivery. Here we report the synthesis of a family of amphiphilic block glycopolymers containing d glucose, d galactose and d mannose via metal-free organocatalyzed ring-opening polymerization of functional cyclic carbonates generating narrowly dispersed products of controlled molecular weight and end-group fidelity, and their application in drug delivery. These glycopolymers self-assemble into micelles having a high density of sugar molecules in the shell, a size less than 100 nm with narrow size distribution even after drug loading, and little cytotoxicity, which are important for drug delivery. Using galactose-containing micelles as an example, we demonstrate their strong targeting ability towards ASGP-R positive HepG2 liver cancer cells in comparison with ASGP-R negative HEK293 cells although the galactose is attached to the carbonate monomer at 6-position. The enhanced uptake of DOX-loaded galactose-containing micelles by HepG2 cells significantly increases cytotoxicity of DOX as compared to HEK293. This new family of amphiphilic block glycopolymers has great potential as carriers for targeted drug delivery.