Antimony telluride (Sb2Te3) compounds are well known as excellent thermoelectric materials and have been recently confirmed as three-dimensional topological insulators. In this letter, we have investigated the anisotropic magneto-transport properties of p-type Bi-doped Sb2Te3 bulk single crystals over a broad range of temperatures, degrees and magnetic fields. Giant magnetoresistance (MR) of up to 230% was observed, which exhibits quadratic field dependences in low fields and becomes linear at high fields without any trend towards saturation. The giant MR also shows strong anisotropy with anisotropy ratio up to 210% in angle-dependent measurements. The giant MR might result from strong intervalley and intravalley scattering of holes and the strong anisotropy is attributable to the anisotropy of hole mobility, relaxation time and effective mass in the Fermi surface. The observed giant anisotropic MR could find applications in Sb2Te3-based anisotropic magneto-electronic devices.