Using the effective mass and parabolic band approximations, we determine analytically the energies of the fundamental and lowest states of a confined electron in paraboloidal quantum lens with infinite confinement potential. Consistent with the axial symmetry, when the separation constant is different of zero the states are twice degenerate. The method has been applied to investigate the evolution of the gap energies of some alloys versus the dot size. The electron localization has also been investigated by using finite element calculations. The method developed in this work could be useful to investigate more deeply the lens-shaped quantum dot.