In this paper, to our best knowledge, it is the first time to present a precise simulation and detailed design of angular correlated color temperature (CCT) distribution of white LEDs covering a range of CCT from 2800K to 6500K. An optimized design of packaging structure with a silicone lens covering a phosphor dome performed an extreme small angular CCT deviation of 105K in the simulation and 182K in a corresponding real sample for a white LED with the CCT near 6500K.