A wavelength-tunable single-longitudinal-mode (SLM) narrow-linewidth thulium/holmium co-doped fiber laser (THDFL) was developed in this study. The lasing wavelength was determined by combining a phase-shifted fiber Bragg grating (PS-FBG) and a uniform FBG (UFBG). SLM oscillation was achieved by incorporating a dual-coupler ring filter with the PS-FBG. At a pump power of 2.0 W, the THDFL exhibited excellent SLM lasing performance with a stable optical spectrum. It operated at an output wavelength of ~2050 nm with an optical signal-to-noise ratio of >81 dB, an output power fluctuation of 0.15 dB, a linewidth of 8.468 kHz, a relative intensity noise of ≤−140.32 dB/Hz@≥5 MHz, a slope efficiency of 2.15%, and a threshold power of 436 mW. The lasing wavelength tunability was validated experimentally by stretching the PS-FBG and UFBG simultaneously. The proposed THDFL had significant potential for application in many fields, including free-space optical communication, LiDAR, and high-precision spectral measurement.