Abstract：Spin-Orbit (SO) coupling, as a fundamental quantum effect, is an essential ingredient in many topological phases of quantum matters, like topological insulator and topological semiconductor. To synthesize 2-dimensional (2D) SO coupling with ultracold quantum gases is one of the keys in the field of quantum simulation to study topological quantum matters. We report here the realization of a robust and highly controllable 2D SO coupling with topological non-trivial band structure. By applying a retro-reflected 2D optical lattice, the synthesized 2D SO coupling has precise inversion and C4 symmetries. The non-trivial band topology of the 2D SO coupling is precisely addressed by both equilibrium and non-equilibrium processes. Winding numbers and topological charges are also extracted from the post-quench evolution. Novel dynamical topological quantum matter is also synthesized. Our studies open the new avenue in quantum simulation to explore exotic topological matters with non-equilibrium dynamics.