In order to better analyze the integrated installation of ground-based large telescopes′ Coude optics system, the error analysis was carried out on three levels, and the "Brownian Bridge" walk was used to establish the Coude optics system error model. Firstly, based on the equation of light path, the optical fuzzy the Coude optics system under the influence of atmosphere disturbed was analyzed. Secondly, the optical blur caused by dynamic error and the accumulation printing through effect of gravity were analyzed. Finally, using the "Brownian Bridge" walk, the error model of the focus position of the Coude optics system was established under the full consideration of error chain closure. The results show that even in the temperature gradient of 0.4 ℃/m, atmospheric disturbances can also cause the deviation of about 0.2″, equaling to the atmospheric coherent length of 2.3 mm. On the other hand, because the symbols of the refractive compensation were consistent, the effects of atmospheric disturbances cannot be compensated by averaging. According to the improved error model, focus position error of the Coude optics system reduce about 20% compared to the results obtained based on the assumption of independent distribution, that is, the error closure was considered more fully.