We herein report the synthesis of highly-fluorescent CdSe/ZnS core-shell quantum dots (QDs) nanophosphors via a simple, non-phosphine and one pot synthetic method in the absence of an inert atmosphere. The as-prepared nanocrystallites were characterized by Fourier transform infrared spectroscopy (FTIR), ultraviolet-visible (UV-vis) and photoluminescence spectroscopy, transmission electron microscopy (TEM) and high resolution TEM (HRTEM). The obtained CdSe/ZnS QDs were of high quality with sharp absorption peaks, bright luminescence, narrow emission width and high PL quantum yield (up to 74 %) without any size sorting. The structural analysis showed that the as-synthesised QDs are small and spherical in shape with narrow size distributions while the presence of the lattice fringe in the HRTEM image confirmed the crystallinity of the material. The dispersion of the obtained core-shell QDs in PMMA matrix resulted in the fabrication of highly fluorescent PMMA- CdSe/ZnS core shell QDs polymer nanocomposite film.