Although for a real high-power and high-energy laser the propagation distance of lasers in the beam control system (or called the inner optical system) is much shorter than that in the long-distance atmosphere, the thermal effect of a high-power-density laser beam passing through the inner optical system remarkably affects the far-field beam quality. By using a four-dimensional simulation code, detailed numerical calculations are performed for the high-power laser propagation in the inner optical system, where an annular profile with linear non-uniformity in the x direction is used to model the high-power laser. The astigmatic parameter, power in the bucket (PIB) and position of the peak intensity are chosen as the parameters for characterizing beam quality in the far-field. It is found that the thermal effect in the inner optical system reduces the peak intensity and beam focusability, thus degrades the far-field beam quality. In addition, the non-uniformity of the initial beam affects the focusability and gives rise to the astigmatism. It is worth noting that the thermal blooming is a nonlinear effect, which affects the intensity distribution and results in a shift of the position of peak intensity in the far-field. The physical interpretation is given and confirmed by numerical results.