Narrow linewidth fiber lasers (NLFLs) are widely employed in application of beam combining. However, the power scaling of the NLFL are severely limited by the transverse mode instability (TMI) effect. In this work, we have verified that the TMI threshold of narrow linewidth fiber amplifier can be enhanced by employing a 981 nm pump scheme. By constructing a 981 nm counter-pumped fiber amplifier, the output power of single mode NLFL is scaled to over 4 kW. In the experiment, the narrow linewidth seed laser is white noise signal phase modulated single frequency laser, and the main amplifier has two types of laser diodes at wavelengths of 976 nm and 981 nm as counter-pump. When the 976 nm laser diodes are employed, the NLFL is scaled to a maximum of 3.4 kW, which is limited by the occurrence of TMI effect. When the 981nm laser diodes are employed, the NLFL is scaled to 4.05 kW without any sign of TMI. The M² factor of the output laser is 1.3. Further power scaling of the fiber amplifier is only limited by the available pump power. By optimizing the fiber laser design and employing bidirectional-pump, NLFL with higher power is achievable.