We demonstrate the operation of Nd:LuLiF 4 laser with efficient 1.31 and 1.32 μm dualwavelength. Maximum continuous-wave output power of 1.63 W is obtained at an incident pump power of 9.97 W and 8% transmission of output coupler (OC), giving a slope efficiency of 17.9%. When monolayer graphene is employed as saturable absorber, stable passively Qswitched 1.31 and 1.32 μm dual-wavelength laser operation still remains. The maximum average output power of 1.33 W, the largest pulse energy of 17.3 μJ and the highest peak power of 111.6 W are achieved with the 8% OC. Meanwhile, the shortest pulse duration of 133 ns and the highest repetition rate of 91 kHz are rendered by the 3.8% OC cavity.