A functionalized poly(amidoamine) (PAMAM) nanocarrier was designed and prepared to deliver anticancer drugs. The nanocarrier is a copolymer with a core-shell structure with 3.0 G PAMAM as the core and sequentially conjugated poly(2-(N,N-diethylamino)ethyl methacrylate) (pDEA) and methoxy-poly(ethylene glycol) 2000 (mPEG) as the shell. The copolymer, PAMAM-pDEA-mPEG, was synthesized using atom transfer radical polymerization and click chemistry. The PAMAM core loaded drugs. pDEA had pH-sensitive properties, showing hydrophobicity in neutral environments and hydrophilicity in weakly acidic environments because of the presence of tertiary amines. Therefore, pDEA was a functional layer coating drugs in neutral environments and releasing drugs in acidic environments. The outer mPEG layer allowed the nanocarrier to circulate in the blood for a long period of time and improved the stability of the nanocarriers. The anticancer drug 5-fluorouracil (5-FU) was entrapped in the nanocarrier at high levels by changing the pH from 4.0 to 8.0. The drug release was also highly pH responsive, and the release rate was much higher at pH 6.5 than at pH 7.4, which favored drug release in the weakly acidic tumor environment. The blank nanocarrier was not toxic to cells or animals. The 5-FU-loaded nanocarrier exerted enhanced anticancer effects on tumor-bearing mice relative to 5-FU alone. PAMAM-pDEA-mPEG is a promising nanocarrier for the delivery of anticancer drugs.