We report the synthesis and characterization of an amphiphilic polymer comprising a hydrophobic palmitoyl (Pal) group and a zwitterionic poly(2-methacryloyloxyethyl phosphorylcholine) (pMPC) block, which is capable of forming micelles as a drug carrier system for delivering hydrophobic anticancer drugs such as doxorubicin (DOX). We hypothesize that the sharp polarity contrast between the Pal domain and the pMPC block would strengthen the micelles and improve the drug loading capacity, while the pMPC shells improve the micelle stability and cellular uptake efficiency. In this study, the Pal-pMPC polymer was characterized and compared with a Pal-poly(ethylene glycol) (Pal-PEG) polymer in terms of their micelle formation, cytotoxicity, and drug loading of DOX. The DOX-loaded Pal-pMPC micelles were further evaluated for the cellular uptake and anticancer activities in cell culture systems including the non-multidrug-resistance HeLa cell line and the multidrug-resistance AT3B-1 cell line. The results showed that the Pal-pMPC polymer had a minimal toxicity. The Pal-pMPC micelles exhibited higher drug loading capacity and enhanced cellular internalization efficiency compared to micelles formed by the Pal-PEG polymer. It was also found that DOX-loaded Pal-pMPC micelles exhibited a more efficient anticancer effect than Pal-PEG micelles in multidrug-resistance cancer cells in an environment with fetal bovine serum.