Structural, vibrational and transport properties of liquid alumina at 2500 K and amorphous alumina at 300 K were studied by molecular dynamics simulations using an empirical Born-Mayer-Huggins potential with the recently optimized parameters. The investigations were conducted for the predicted densities at almost zero pressure, as well as the experimentally reported densities of 2.81 g/cm3 and 3.175 g/cm3. A detailed examination of the interatomic correlations showed that for both liquid and amorphous alumina, the short-range order was dominated by the slightly distorted (AlO4)5− tetrahedra. Vibrational density of states (VDOS) was obtained from the Fourier transform of the velocity autocorrelation functions (VACF), which exhibited broader ranges for the liquid phases compared with those for the amorphous phases. Each VDOS spectrum was divided into two primary frequency bands for both liquid and amorphous alumina. Thermal conductivities (κ) and viscosities (η) were estimated respectively through the heat-current autocorrelation functions (HCACFs) and stress autocorrelation functions (SACF) by the equilibrium molecular dynamics (EMD) simulations using the Green-Kubo relation. And the results were shown to be consistent with the experimental data, especially that κ was equal to 2.341 ± 0.039 Wm−1K−1 for amorphous alumina at 2.81 g/cm3 and 300 K, η was equal to 0.0261 ± 0.0017 Pa·s and 0.0272 ± 0.0018 Pa·s for the liquid phases at 2500 K with densities of 2.81 g/cm3 and 2.863 g/cm3, respectively. Mean squared displacements (MSDs) were employed for the self-diffusion coefficients (D) estimation.