We investigate Rashba spin-orbit coupled Fermi gases in square optical lattice by using the determinant quantum Monte Carlo (DQMC) simulations which is free of the sign-problem. We show that the Berezinskii-Kosterlitz-Thoules phase transition temperature is firstly enhanced and then suppressed by spin-orbit coupling in the strong attraction region. In the intermediate attraction region, spin-orbit coupling always suppresses the transition temperature. We also show that the spin susceptibility becomes anisotropic and retains finite values at zero temperature. Introduction: Spin-orbit coupling (SOC), breaking the inversion symmetry, has attracted extensive attentions in condensed matter [1,2]. Recently, SOC in both the bosonic [3,4] and fermionic [5,6] systems has been realized in ultracold atomic experiments. These milestone breakthroughs have opened up an exciting route to study the novel phases [7][8][9][10][11][12][13][14][15] induced by SOC in these systems.By introducing SOC, two dimensional (2D) fermionic systems exhibit much more rich phenomena [16][17][18][19][20]. SOC can stabilize the topological nontrivial superfluid states [21][22][23][24]. Majorana zero mode exists in the vortices of these topological nontrivial phases and plays a crucial role in topological quantum computation [25]. It was found that SOC has nontrivial effect on pairing and superfluidity [22,26] in homogeneous systems. SOC enhances the pairing but suppresses the superfluidity. On lattice, SOC exhibits opposite filling-dependent behaviors for the superfluidity [27]. These interesting physics induced by SOC are all investigated by the Bogoliubovde Gennes (BdG) approach. Moreover, the study of the spin-orbit coupled Fermi gases in lattice at finite temperature is still waiting to be explored.Two effects are resulted by applying SOC in the Fermi Hubbard model. First, SOC enhances the effective hopping amplitude and enlarges the bandwidth. The other is that SOC flips the spin of the fermion which breaks the rotational symmetry of the spin and significantly changes the properties of the Fermi surface. When the system only contains the SOC, the ground state is semimetal near half-filling[27] with vanishingly small density of state(DOS)(ρ(E) ∼ |E|). In the strong attractive limit, the fermions are strongly bounded and the superfluid transition temperature is determined by the center-ofmass motion which is proportional to the inverse of the attraction. Therefore, our major concern here is to investigate what effects can be induced by the SOC on the pairing at finite temperature beyond the BdG approach.In this Letter we investigate the pairing of the attractive Fermi gases in 2D square optical lattice with SOC using both DQMC simulations [28][29][30][31][32] and mean field theory. To our knowledge, this is the first unbi-