We have theoretically investigated the influence of antireflective sub-wavelength structures on a monolithic white light-emitting diode (LED). The simulation is based on the rigorous coupled wave analysis (RCWA) algorithm, and both cylinder and moth-eye structures have been studied in the work. Our simulation results show that a moth-eye structure enhances the light extraction efficiency over the entire visible light range with an extraction efficiency enhancement of up to 26 %. Also for the first time to our best knowledge, the influence of sub-wavelength structures on both the color rendering index (CRI) and the correlated color temperature (CCT) of the monolithic white LED have been demonstrated. The CRI of the monolithic white LED could be improved from 92.68 to around 94 by applying a cylinder structure, and the CCT could be modified in a very large range with appropriate design of the cylinder structure.