The very-large-mode-area (VLMA) fiber is of great importance for suppressing the nonlinear effects which are considered as main limitations to the power scaling-up of high-power fiber lasers and amplifiers. The thermally guiding (TG) VLMA fiber is a novel VLMA fiber, the waveguide of which is formed by the thermal lens effect. Then, a low numerical aperture can be realized, which is promising to achieve the expanding of mode area with a high-quality beam. In order to study the performance of TG VLMA fiber in a fiber amplifier, we present a rate-equation model of the single-mode ytterbium-doped TG VLMA fiber amplifier, which consists of the steady-state rate equations and thermal transferring equations. With this model, the forward-pumped single-mode TG VLMA fiber amplifier is numerically studied. It is found that the diameter of fundamental mode field rises with the increase of the signal power, which shows the superiority of the TG VLMA fiber in suppressing the nonlinear effect in the fiber amplifier. The optimum fiber length and pertinent physical mechanism are also investigated. It is revealed the optimum fiber length is related to the input pump power, and it decreases with the increase of input pump power. However, when the input pump power is large enough, such a variation of optimum fiber length will become weakened. The numerical results also illuminate that the thermal load at the optimum length of TG VLMA fiber should not change too much with the input pump power. Moreover, the mode of output optical field is also discussed. It is found that the thermal load at the optimum length may not be large enough to realize a core-confined mode. In order to ensure that the core-confined mode can be output, the thermal load at the end of the fiber amplifier should be larger. It requires that the fiber length used in the amplifier should be shorter than the optimum fiber length, which will induce the decrease of the output signal power to some extent. In spite of that, the numerical results reveal that the decrease of output signal power should not be much, and the pertinent slope efficiency is not obviously lowered, either. Thus, it is verified that the core-confined mode with a VLMA can be obtained from the TG VLMA fiber amplifier with high slope efficiency. The pertinent results have significant guidance in the design of TG VLMA fiber amplifier.