The functionalization approach for nanomaterials is of great importance for their application in drug delivery systems. Herein, an approach based on block copolymer installation into polymer nanogels was newly developed. Poly(vinyl alcohol)-incorporated polymer nanogels were prepared by a two-step dispersion/precipitation polymerization. Poly(methacrylic acid)-block-poly(3-fluorophenylboronic acid methacrylamide) (PMAA-b-PFPBMA) prepared by two-step reversible addition-fragmentation chain transfer polymerization was installed into the polymer nanogels via boronate ester formation. Furthermore, cisplatin as a cancer therapeutic drug was successfully loaded on the block copolymer-installed polymer nanogels, and cell death was achieved by using the resulting cisplatin-loaded nanogels. We believe that the functionality of the nanogels can be changed by varying the installed block copolymer, leading to the functionalization approach of polymer nanogels based on block copolymer installation, which will be of great utility in many fields.