The structures of three-electron systems of three-dimensional quantum dots are investigated via an analysis of quantum mechanical symmetry and the possibility of magic numbers exitence is pointed out. We compared it with the magic numbers of three-electron systems of two-dimensional quantum dots. Within the effective-mass approximation, the energy spectra of three-electron systems in a parabolic potential (?ω0=2meV) are calculated. The results show that there is the trace of the magic numbers exitence. The ground state of three-electron systems of three-dimensional quantum dots is 1- state.