One of the most outstanding limitations in the evolution of the power scaling of fiber laser with near diffraction limited beam quality has been the mode instability since it was found in 2010. For a long time, researchers have focused on the dynamic mode instability (DMI) theoretically and experimentally, and it was not until 2016 that a new analytical model called quasi-static mode instability (QSMI) was proposed. Unlike DMI, because of the one-way energy transfer characteristic on a specific time scale, QSMI will show no apparent fluctuations with respect to the time domain traces. In this paper, based on a counter-pump few-mode fiber amplifier schematic system, the output power, beam quality and time traces of the amplifier under changing seed laser power are measured to investigate its mode instability effect. The ytterbium-doped fiber of the amplifier has a core diameter of 25 μm and inner cladding diameter of 400 μm, which can support 4-5 modes to be transmitted in the amplifier. The experimental results reveal that QSMI happens in the few-mode fiber amplifier. Taking 234 W seed power for example, it is found that when the output power reaches 2030 W, the optical-to-optical efficiency begins to fell from 86% to 32%, and at the same time the M2 value has an abrupt degradation from 2.2 to 2.8, which indicates that MI happens. On the other hand, it can be seen from the time traces of the output laser that there exist no rapid fluctuations, and the Fourier analysis shows no sign of DMI characteristic frequency components either. Quoting the definition of drifting ratio σ, when the output power is 2030 W under 234 W seed power, it is only 4%, and thus verifying that it is QSMI instead of DMI. The experiment also indicates that increasing the seed power has an effective influence on enhancing the mode instability power. When the seed power is raised from 86 W to 528 W, the corresponding threshold power is increased from 1560 W to 3090 W. And for 528 W seed power, when the output laser surpasses 3000 W, the optical-to-optical efficiency does not decline as fast as other relatively low seed power. To sum up, the mode instability effect represents a kind of quasi-static property in these large core diameter few-mode fiber amplifiers, which needs further studying.