Highly luminescent CdSe/CdxZn1-xS core-shell quantum dots (QDs) were synthesized using CdSe cores with the size range of 2 to 5 nm in diameter through a facile organic route. The CdSe cores were prepared by using trioctylphosphine oxide and hexadecylamine as capping agents for the purpose of getting spherical morphology. The cores were coated with an alloy shell to decrease the lattice mismatch between the core and the shell through a facile organic approach. The QDs exhibited tunable photoluminescence (PL) up to 654 nm, narrow PL spectra (less than 40 nm for full width at half maximum) and high PL efficiency. Such properties make the core-shell QDs as a good candidate for further applications.