In this paper, we propose a quantum dot (QD) based white light emitting diode (WLED) structure to study theoretically the material gain and quantum efficiency of the system. We consider the spherical QDs with a II–VI semiconductor core (CdS) that covered with a wider band gap semiconductor acting as a shell (ZnS). In order to generate white light spectrum, we use layers with different dot size that can emit blue, green and red colors. The blue emission originating from CdS core combines to green/orange components originating from ZnS shell and creates an efficiency white light emission. To model this device, at first, we solve Schrödinger and Poisson equations self consistently and obtain eigen energies and wave functions. Then, we calculate the optical gain and internal quantum efficiency (IQE) of a CdS/ZnS LED sample. We investigate the structural parameter effects on the optical properties of the WLED. The numerical results show that the gain profile and IQE curves depend strongly on the structural parameters such as dot size, carrier density and volume scaling parameter. The gain profile becomes higher and wider with increasing the core radius while it becomes less and narrower with increasing the shell thickness. Furthermore, it is found that the volume scaling parameter can manage the system quantum efficiency.