Stepped-horn antenna loaded with dielectric material of variable permittivity is proposed to improve radiation characteristics and/or to increase the electrical dimensions of the radiating structure compared to unloaded empty one. A hybrid numerical technique is used to analyze such an antenna. The tapered section of the horn antenna is modeled by multi-stepped waveguide structures filled with variable dielectric constant material. Generalized scattering matrix representation of the tapered section of the horn antenna is obtained using mode matching technique. The radiating aperture problem is solved by the method of moments, under the assumption that the horn is terminated by an infinite metallic flange. Input return loss, gain, aperture efficiency and cross-polarization characteristics are studied. Comparisons indicate that any kind of loading with dielectric material along the taper tend to improve the gain level for the entire bandwidth, aperture efficiency may increase and cross-polarization level may decrease for relatively narrow bandwidths. It is observed that this is partly due to increase in the electrical size of the aperture and partly due to excitation of higher order modes. The goal of the optimization in a stepped-horn antenna is to adjust the magnitude and phase of the excited TE₃₀ mode to achieve more uniform aperture field distribution. This has been accomplished by optimizing step length and permittivity of the enclosed dielectric material. As a result of optimization, improved gain, reduced cross-polarization and enhanced aperture efficiency characteristics have been achhieved in a stepped-horn antenna. Instead of loading only one material, using materials with different permittivities gave extra parameters to control characteristics such as the input return loss. These study can be extended for further multi-stepped structures with variable dielectric materials.