By means of transfer matrix method, the reflection band gap of Thue-Morse(T-M) structure containing anisotropic left handed material was studied.The influence of incident angle, polarization and lattice scaling factor on reflection band gap was theoretically investigated.It is shown that there is an Omnidirectional Reflection Band (ORB) in the structure.The width of the ORB is determined by the higher frequency band edge for TE polarization and the lower frequency band edge for TM polarization.When an impurity is introduced, a defect mode appears in the reflection band gap.The position of the defect modes is weakly dependent on incident angle for TE polarization, but affected by incident angle for TM polarization.