Compared to zig-zag solid-state slab lasers, zig-zag solid-state tube lasers (SSZTLs) exhibit significant potential in beam quality improvement and output power enhancement. However, the progress of SSZTLs still faces enormous challenges due to the lack of effective control of beam quality. We first developed a comprehensive model for analyzing the output beam quality of zig-zag tube lasers by taking both the fabrication and alignment errors and thermal effects into consideration. The primary factors degrading the beam quality and thermal stability of the SSZTLs were analyzed in detail, and a self-correction method based on the complementary optical path was further proposed and analyzed theoretically to effectively improve the beam quality and thermal stability of the SSZTLs. The results show that this method can not only effectively correct the off-axis aberrations but also mitigate the depolarization loss that arises from the thermal instability of the SSZTLs. This work can provide a reference in the beam control and applications of SSZTLs.