THz time-domain spectroscopy (THz-TDS) is used to study the THz-optical properties of a single crystal bismuth ferrite BiFeO3 (BFO). It can be found that the anisotropy of BiFeO3 is strongly dependent on the temperature. A giant birefringence up to around 3.6 is observed at 1 THz. The presence of a spatially modulated cycloidal antiferromagnetic structure leads to spin cycloid resonances (SCR) ψ and Φ, corresponding to the out-of-plane and in-plane modes of the spin cycloid, respectively. We distinguish the SCR with respect to their response to orthogonal polarizations of the electric fields of the incident THz beam. In addition, we observe a resonance appearing below 140 K, which might be interpreted as an electromagnon mode and related to a spin reorientation transition. Our present observations present that the temperature and polarization, as the external control parameters, can be used to modulate the THz optical properties of BFO single crystal.