We first report a diode-pumped continuous wave orthogonally polarized dual-wavelength single-longitudinal-mode laser with a single c-cut Tm,Ho:LuLiF₄ laser crystal. The simultaneous dual-wavelength single-longitudinal-mode laser near 2 μm is realized by using two uncoated intracavity Fabry-Perot etalons. The output wavelengths are 2064 nm in π-polarization and 2066 nm in σ-polarization respectively, which are orthogonal to each other. At the absorbed pump power of 1 W, the maximum single-longitudinal-mode output powers at 2064 and 2066 nm are 76 and 32 mW respectively. The orthogonally polarized dual-wavelength single-longitudinal-mode laser is possible to be applied to the 2 μm differential absorption lidar and the generation of THz radiation.