Dual-responsive amphiphilic block copolymers were synthesized by combining enzymatic ring-opening polymerization (eROP) of ${varepsilon}$-caprolactone (CL) and ATRP of N,N-dimethylamino-2-ethyl methacrylate (DMAEMA). The obtained block copolymers were characterized by gel permeation chromatography (GPC), $^1H$ NMR and FTIR-IR. The critical micelle concentration (CMC) of copolymer was determined by fluorescence spectra, it can be found that with hydrophilic block (PDMAEMA) increasing, CMC value of the polymer sample increased accordingly, and the CMC value was 0.012 mg/mL, 0.025 mg/mL and 0.037 mg/mL for $PCL_{50}$-b-$PDMAEMA_{68}$, $PCL_{50}$-b-$PDMAEMA_{89}$, $PCL_{50}$-b-$PDMAEMA_{112}$, $PCL_{50}$-b-$PDMAEMA_{89}$ was chosen as drug carrier to study in vitro release profile of anti-cancer drug (taxol). The temperature and pH dependence of the values of hydrodynamic diameter (Dh) of micelles, and self-assembly of the resulting block copolymers in water were evaluated by dynamic light scattering (DLS). The result showed that with the temperature increasing and pH decreasing, the Dh decreased. Drug-loaded nanoparticles were fabricated using paclitaxel as model. Transmission electron microscopy (TEM) and atomic force microscopy (AFM) had been explored to study the morphology of the hollow micelles and the nanoparticles, revealing well-dispersed spheres with the average diameters both around 80 nm. In vitro release kinetics of paclitaxel from the nanoparticles was also investigated in different conditions (pH and temperature, etc.), revealing that the drug release was triggered by temperature changes upon the lower critical solution temperature (LCST) at pH 7.4, and at $37^{circ}C$ by an increase of pH.