Targeted and efficient delivery of therapeutics to tumor cells is one of the key issues in cancer therapy. In the present work, we report a temperature and pH dual responsive core-shell nanoparticles comprising smart polymer shell coated on magnetic nanoparticles as an anticancer drug carrier and cancer cell-specific targeting agent. Magnetite nanoparticles (MNPs), prepared by a simple coprecipitation method, was surface modified by introducing amine groups using 3-aminopropyltriethoxysilane. Dual-responsive poly(N-isopropylacrylamide)-block-poly(acrylic acid) copolymer, synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization, was then attached to the amine-functionalized MNPs via EDC/NHS method. Further, to accomplish cancer-specific targeting properties, folic acid was tethered to the surface of the nanoparticles. Thereafter, rhodamine B isothiocyanate was conjugated to endow fluorescent property to the MNPs required for cellular imaging applications. The nanoparticles were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), selected area electron diffraction (SAED), field emission scanning electron microscopy (FESEM), energy-dispersive X-ray spectroscopy (EDX), thermogravimetric analysis (TGA), zeta potential, vibrating sample magnetometer (VSM), X-ray photoelectron spectroscopy (XPS) measurements, and FTIR, UV-vis spectral analysis. Doxorubicin (DOX), an anticancer drug used for the present study, was loaded into the nanoparticles and its release behavior was subsequently studied. Result showed a sustained release of DOX preferentially at the desired lysosomal pH and temperature condition. The biological activity of the DOX-loaded MNPs was studied by MTT assay, fluorescence microscopy, and apoptosis. Intracellular-uptake studies revealed preferential uptake of these nanoparticles into cancer cells (HeLa cells) compared to normal fibroblast cells (L929 cells). The in vitro apoptosis study revealed that the DOX-loaded nanoparticles caused significant death to the HeLa cells. These nanoparticles were capable of target specific release of the loaded drug in response to pH and temperature and hence may serve as a potential drug carrier for in vivo applications.