For laser ablation propulsion’s applications in space (e.g., space-debris removal, etc.), the laser power is well above the critical power for self-focusing in the atmosphere. Therefore, the self-focusing effect on the beam quality is very significant. In addition, a high-power laser beam is usually accompanied with spherical aberration due to nonlinear effects in its generation process. In this paper, the influence of spherical aberration on the beam quality of high-power laser beams propagating upwards in the atmosphere is studied by using numerical simulation. It is shown that for the large beam size case, the target intensity may be improved by applying the positive spherical aberration. However, for the small beam size case, the target intensity may be improved by using the negative spherical aberration. Furthermore, a laser beam with a large size is more suitable for laser ablation propulsion’s applications in space than that with a small size. Owing to the linear diffraction effect and the nonlinear self-focusing effect, there exists optimal beam power to maximize the target intensity. The formula of the optimal beam power is fitted for the large beam size case in this paper. On the other hand, the focal shift appears due to diffraction, self-focusing and spherical aberration, which results in a degradation of the beam quality on the target. For the large beam size case, to move the actual focus to the target and improve the beam quality on the target, the formula of the modified focal length is also derived in this paper. The results obtained in this paper are of important theoretical significance and practical value.