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Cold atoms with laser-induced spin-orbit(SO)interactions provide intriguing new platforms to explore novel quantum physics beyond natural conditions of solids.In the work presented here we propose in theory and realize in experiment 2D SO coupling and topological band for 87Rb quantum degenerate gas through an optical Raman lattice,without phase locking or fine tuning of optical potentials.A controllable crossover between 2D and 1D SO couplings is studied,and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in momentum space.