A numerical analysis has been performed for natural convection in an air conditioner duct system. The governing equations were solved a finite volume method using a SIMPLE algorithm. In the calculation mode of duct, the room temperature was preserved at $25.0^{circ}C$ and duct wall temperature had a temperature of 15, 20.0, 22.5, 23.75, 26.25, 27.5 30 and $35^{circ}C$. The results of velocity vectors and contours have been represented for various parameters. Based on the numerical data, the relationships between temperature difference and flow rate into room was represented. In the case of $T_gamma>T_omega$, the equation for temperature difference and flow rate was $Q=0.0285 riangleT^0.4005$, and in the case of $T_gamma>T_omega$, the equation was $Q=0.0099 riangleT^0.4752$. The duct system has an important relation to room temperature and duct wall temperature.