The invention is a nanoparticle that contains an anticancer drug that is released in cancer cells when administered to a subject. The nanoparticles have a core including the anticancer drug and polymer chains that are soluble at the pH of the cancer cell. The core is surrounded by a layer of polymer chains that are insoluble at the pH of healthy tissue but soluble at the pH of the cancer interstitium. An outside layer is made of water-soluble polymer chains to shield the nanoparticle from RES recognition and give the nanoparticle a long circulation time in the bloodstream of the subject. The outside layer may also include folic acid moieties that bind folic acid receptors on the surface of the cancer cell.