We present the prompt BAT and afterglow XRT data of Swift-discovered GRB081109A up to ~ 5\times 10^5 sec after the trigger, and the early ground-based optical follow-ups. The temporal and spectral indices of the X-ray afterglow emission change remarkably. We interpret this as the GRB jet first traversing the freely expanding supersonic stellar wind of the progenitor with density varying as $\rho \propto r^{-2}$. Then after approximately 300 sec the jet traverses into a region of apparent constant density similar to that expected in the stalled-wind region of a stellar wind bubble or the interstellar medium (ISM). The optical afterglow data are generally consistent with such a scenario. Our best numerical model has a wind density parameter {$A_{*} \sim 0.02$, a density of the stalled wind $n\sim 0.12 {\rm cm}^{-3}$, and a transition radius $ \sim 4.5 \times 10^{17}$ cm}. Such a transition radius is smaller than that predicted by numerical simulations of the stellar wind bubbles and may be due to a rapidly evolving wind of the progenitor close to the time of its core-collapse.