A large-area two-dimensional Thue-Morse quasicrystal with nanometer structures is fabricated on poly-methyl methacrylate (PMMA) substrate using the technology of electron beam lithography (EBL). And the optical properties of sample are studied by the far-field diffraction experiment. In addition, according to the diffraction principle and interference theory, the Fraunhofer diffraction patterns of the Thue-Morse quasicrystal are simulated and analyzed. It is shown that the theoretical simulations are consistent with the experimental results very well.