The spectral characteristics of aluminium oxide (Al₂O₃) in broadband terahertz wave range (0.2~3.0 THz) were investigated by using terahertz time-domain spectroscopy (THz-TDS). The terahertz time-domain spectra of Al₂O₃ crystal at different azimuthal angles is obtained by changing the angle between the crystal optical axis and the polarization direction of THz pulse. The refractive index and absorption coefficient of o- and e-waves are calculated, and the index ellipse of Al₂O₃ in THz band is drawn. The experimental results indicate that Al₂O₃ has large birefringence and low absorption coefficient in THz, with a birefringence as high as 0.36 and an absorption coefficient lower than 5 cm^-1. The phase and amplitude of THz pulse can be modulated based on the birefringence of the crystal. Al₂O₃ crystal can be used as "shaper" of THz pulse, which provides important reference for the application of terahertz wave in ultra-wideband and ultra-high speed communication systems.