A highly efficient design procedure for dielectric-loading multi-band coaxial-type feed antennas is proposed in this paper. Cylindrical modal matching method is employed for generalized scattering matrix calculation inside the feed, while spherical wave expansion is adopted for the feed aperture discontinuity in consideration of the outer shape. Closed-form scattering matrices with respect to different junctions help realize higher computational efficiency than the full-wave simulation solvers, and thus enable rapid optimization in terms of various electrical functional requirements across multiple frequency bands simultaneously. A Ku/Ka multi-band feed is investigated as a numerical example. Excellent radiation performances, including the low cross-polarization level, constant beamwidth, stable phase center, high return loss, and high isolation between bands of interest are achieved by employing multi-scalar rings, dielectric loading, and a three-port hybrid junction. The design is validated by experimental results from a manufactured prototype. Good consistency confirms the accuracy of our numerical approach, and demonstrates the proposed feed a good candidate for Ku/Ka-band satellite communication antenna systems.