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We demonstrate a compact wavelength-tunable and -switchable mode-locked Yb-doped fiber (YDF) laser based on single-walled carbon nanotube (SWCNT) wall paper absorber. Two mechanisms coexist in the fiber cavity. The switchable mode-locked state can be obtained between two wavelengths depending on the fiber-loop-induced cavity birefringence. Because of the intensity-dependent transmission distribution, the proposed fiber laser can be operated in the tunable wavelength mode-locked state from 1025 to 1037 nm. The spectral bandwidth varied from 1.1 to 2.4 nm depending on the operating wavelength and the pump power with pulse duration of hundreds of picoseconds. The average wavelength spacing is 3.6 nm, which can be changed, corresponding to the birefringence of the fiber cavity. Moreover, stable wavelength-tunable mode locking is obtained at room temperature.