La1-xMgxO1-2xF2xBiS2 (x = 0.1-0.35) were synthesized, and their superconductive properties were investigated. The superconducting transition temperature (T-c) increased below the codoping level (x <= 0.25). La1-xMgxOBiS2 (x = 0-0.2) and La1-xMgxO0.6F0.4BiS2 (x = 0.1-0.3) were further prepared to explore the effect of Mg2+. We found that the introduction of Mg2+ and F- leads to local structure distortion. Larger distortion is beneficial for superconductivity in LaOBiS2, which was further confirmed by the results in La1-xCaxO1-2xF2xBiS2 (x = 0.2, 0.3).