Colloidal core/shell semiconductor nanocrystals have attracted considerable interest in recent days due to their immense potential in wide range of applications as biological fluorescent labels, bio imaging, light emitting diodes, solar cells etc. In this paper, we describe a simple synthetic route for the development of high quality CdSe/ZnSe core/shell quantum dots capped in aqueous solutions with the biocompatible polymer of L-cysteine is presented. The crystal structure, morphology, spectral and compositional properties were analyzed from powder X-ray Diffraction, High resolution transmission electron microscopy (HRTEM), UV-Vis absorbance and Photoluminescence (PL), Fourier transform infrared (FTIR) and Fourier transform RAMAN (FT-RAMAN) techniques. The XRD results depicted the formation of zinc blende structured CdSe/ZnSe quantum dots with the average crystallite size of 5 nm and 4 nm, which is in accordance with observations from HRTEM micrographs. The UV-Vis absorbance peaks indicate the broad absorption behavior of the synthesized CdSe/ZnSe quantum dots. The photoluminescence studies evidenced that the luminesce property of quantum dots can be varied by systematically tuning the core and shell precursor concentrations. The capping of ZnSe and L-cysteine was confirmed from FTIR and FT-RAMAN studies.