The single-scattering properties of randomly oriented triaxial ellipsoids with size parameters from the Rayleigh to geometric-optics regimes are investigated. A combination of the discrete dipole approximation (DDA) technique and an improved geometric optics method (IGOM) is applied to the computation of ellipsoidal particle scattering properties for a complete range of size parameters. Edge effect con tributions to the extinction and absorption efficiencies are included in the present IGOM simulation. It is found that the extinction efficiency, single-scattering albedo, and asymmetry factor computed from the DDA method for small size parameters smoothly transition to those computed from the IGOM for moderate-to-large size parameters. The phase matrix elements computed from these two methods are also quite similar when size parameters are larger than 30. Thus, the optical properties of ellipsoidal particles can be computed by combing the DDA and the IGOM for small-to-large size parameters. Furthermore, we also examine the applicability of the ellipsoid model to the simulation of the scatter ing properties of realistic aerosol particles by comparing the theoretical and experimental results for feldspar aerosols. It is shown that the ellipsoid model is better than the commonly used spheroid model for simulating dust particle optical properties, particularly, their polarization characteristics, realistically.