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Exhaust smoke discharged from marine vessels and offshore plants not only contaminates the hull and cargo but is also the main cause of deterioration in the crew’s health and working environment. Rules and regulations have been implemented and have become stricter in recent decades. In this study, the exhaust smoke flow around an anchor-handling tug supply vessel in a stationary state, which has been seldom studied, is analyzed using computational fluid dynamics. The study investigates the effect of changing the wind speed and direction, which primarily affects the flow and dispersion of the smoke, to verify the suitability of the environment for the crew. To assess the environment, the recommended and comfortable concentrations of NO2 are used. The results demonstrate that a higher wind speed worsens the effect of the exhaust flow on the environment, owing to lower-pressure values and regions behind the structures. The emission of exhaust smoke is unsatisfactory when the wind flows from the side or rear of the vessel, instead of from the bow. Differing from previous studies conducted on general merchant vessels in navigating conditions, it was found that side winds can also have detrimental environmental effects in the stationary state. Adopting the original design of exhaust pipes leads to the distribution of exhaust smoke over the deck, exceeding the recommended exposure limit. Increasing the height of the pipes is identified as a simple but effective method to facilitate the smooth discharge of exhaust smoke.