A biodegradable brush-type copolymer PHF- g-(PCL-PEG) based on a cleavable polyacetal backbone and biodegradable side chain modified with polyethylene glycol (PEG) was synthesized in this paper. This particular structure was directional to facilitate the formation of spherical or rod-shaped micelles. Flow cytometry showed that rod-shaped micelles displayed enhanced cellular uptake compared to spherical micelles. Rod-shaped micelles were selected to investigate their drug delivery abilities in detail. In vitro experiments verified the pH-triggered drug release of DOX-loaded micelles, and the release rate of doxorubicin (DOX) was 77% at pH 5.0 and 26% at pH 7.4. In drug-release kinetic analysis, a double-exponential model achieved the best fit. The copolymer appeared to be almost nontoxic, while the DOX-loaded micelles showed equivalent cytotoxicity compared to DOX at high concentration. The endocytosis of DOX-loaded micelles was two times that of DOX. Our findings suggest that the pH-sensitive brush type copolymer could be a possible carrier in drug delivery.