High-power linearly polarized narrow linewidth fiber lasers hold broad application prospects in wavelength beam combining, coherent detection, and other fields. In such lasers, transverse mode instability (TMI) is one of the main factors limiting their power scaling. In this paper, the influence of the TMI effect on the output power of high-power linearly polarized narrow linewidth fiber lasers is analyzed, and a TMI suppression method is proposed. The experiment employs multi-wavelength pumping technology, using 100 mW single-frequency laser as the seed source. The linewidth of the seed source is broadened to 23 GHz via a phase modulator, and after three-stage amplification, a linearly polarized narrow linewidth laser output is finally achieved with the following parameters: power of 2.54 kW, linewidth of 23 GHz, central wavelength of 1064 nm, extinction ratio of 98%, and beam quality factors M_x² = 1.21 and M_y² = 1.23. The influence of pump wavelength on the TMI effect is further analyzed. Due to the small core diameter of the fiber (20 μm) and the high absorption coefficient of the gain fiber for pump light (1.8 dB/m@976 nm), the core temperature increases significantly. Additionally, the heat introduced by the pump photon quantum defect causes a variation in the refractive index of the fiber core, leading to the occurrence of TMI at relatively low power levels. When the pump wavelength is shifted to longer wavelengths, both the quantum defect of the pump light and the pump absorption coefficient decrease, resulting in reduced heat distribution across the entire fiber length as well as per unit length. This thus increases the TMI threshold and effectively improves the output power of the linearly polarized narrow linewidth fiber laser.