Based on the time-harmonic electromagnetic field and waveguide theory, the analytical expressions for the field components of the spherical transverse-magnetic (TM) and transverse-electric (TE) modes inside a metallic hollow conical waveguide with a sub-wavelength-sized exit hole have been derived. The time-averaged electromagnetic field energy density distribution associated with light transmission and the transmission properties of the spherical TM and TE modal fields inside a sub-wavelength hollow conical waveguide have been studied in detail. Moreover, by using the accurate eigenvalues obtained numerically, the influence of the light wavelength, the taper angle, the aperture diameter as well as the length of the conical waveguide on the time-averaged energy density distribution inside the sub-wavelength metallic hollow conical waveguide has been discussed. The results show that the time-averaged energy density distribution inside the conical waveguide varies quasi-periodically. The quasi-period has relation with the mode, the light wavelength as well as the taper angle. Furthermore, there is a clearly pronounced maximum in the radial dependence. The position of an appreciable maximum for the time-averaged energy density varies rapidly with the light wavelength and the taper angle.