Si/SiO2 core/shell quantum dots (QDs) have been shown with wavelength-tunable photoluminescence in addition to their inert, nontoxic, abundant, low-cost, biocompatible advantages. Due to their big size, here, we apply density-functional tight-binding (DFTB) method to perform calculations to study their structures and properties. We systematically investigate the effects of surface passivation, thickness of SiO2 shell, and Si/O ratio on the structures and properties of Si/SiO2 core/shell quantum dots. We find that hydroxyl passivated Si/SiO2 core/shell quantum dots are able to stabilize the quantum dots compared with hydrogen passivated Si/SiO2 core/shell quantum dots. By using DFTB method, we are able to study Si/SiO2 core/shell quantum dots of big size (3 nm) and we find that, in Si/SiO2 core/shell quantum dots, there are competing effects between quantum confinement (blueshift) and oxidation (redshift) with the decrease of the size of Si core. The transition point is when Si/SiO2 ratio is around 1:1. The effect of the thickness of SiO2 on energy gap is not as significant as the effect of the size of the Si core. Our study provides theoretical basis for designing Si quantum dots with tunable photoluminescence.