The quasistatic and dynamic compressive mechanical properties of textured polycrystal sheet of hot rolled TB2-titanium alloy were investigated by Instron apparatus and Split-Hopkinson pressure bar (SHPB) technology, respectively. Cylindrical specimens of textured titanium alloy sheet, which were cut with the cylinder axis along the rolling direction (RD), transverse direction (TD) and 45o direction (RD-45o) from the rolling direction lying in the rolling plane, were compressed at strain rates in the range of 10-3 to 103 s-1. The compressive stress-strain curves show that the flow stresses for different directions of hot rolled TB2-titanium alloy sheet increase with increase of the strain rate and the obvious effect of strain rate hardening is observed. Both the quasistatic and dynamical compressive mechanical properties exhibit anisotropy. Furthermore, the behavior for quasistatic compression is different from that for dynamical compression. Taking into account of possible mechanisms for quasistatic and dynamic plastic deformation, the mechanical anisotropy of textured polycrystal titanium alloy sheets was discussed based on the microscope crystal plasticity deformation theory