A low-cost, wavelength-tunable single-longitudinal-mode (SLM) thulium–holmium co-doped fiber laser (THDFL) in a 2 μm band with a simple structure is described in the present paper. To obtain a stable SLM and narrow laser linewidth, a five-coupler-based three-ring (FCTR) filter is utilized in the ring cavity of the fiber laser. Tunable SLM wavelength output from THDFLs with kHz linewidths can be achieved by designing the FCTR filter with an effective free-spectral range and a 3 dB bandwidth at the main resonant peak. The measurement results show that the laser is in the SLM lasing state, with a highly stabilized optical spectrum, a linewidth of approximately 9.45 kHz, an optical signal-to-noise ratio as high as 73.6 dB, and a relative intensity noise of less than −142.66 dB/Hz. Furthermore, the wavelength can be tuned in the range of 2.6 nm. The proposed fiber laser has a wide range of applications, including coherence optical communication, optical fiber sensing, and dense wavelength-division-multiplexing.