Group II-VI semiconductor quantum dots (Q-dots) have found various applications in biomedical field during last decade. In this study, we have synthesized CdSe Q-dots and CdSe/ZnS core/shell (CS) by wet chemical route and characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), dynamic light scattering (DLS), Fourier-transform infrared spectroscopy (FT-IR) and Photoluminescence (PL) spectroscopy. CS formation was confirmed by red shift as well as enhancement in the luminescence peak compared to bare Q-dots. Processing parameters such as core and sulfur concentrations were optimized at maximum luminescence efficiency during the shell preparation. Effects of dialysis, aging and cell culture medium on the properties of the Q-dots and CS were also studied by luminescence and DLS techniques. DLS data showed Q-dots and CS to be stable, and there was no effect on the integrity of the Q-dots and CS after various modifications. CS was found to be hemocompatible and cytocompatible for human umbilical vein endothelial cells even at a high concentration of 0.1 mg/ml up to 48 h indicating high potential for CS in various biomedical applications.