A loop duct system is often found in a VAV-HVAC(variable air volume heating, ventilating and air conditioning) design. It is known that the simple T-method is not be applicable to the loop duct system and cannot be used to calculate the flow rate and the pressure drop at each duct section of the loop duct system. In this paper, the extended T-method has been developed and it is found to be applicable to the loop duct system to which the simple T-method cannot be applied. The validity of the extended T-method has been verified by using to solve for a simple, ideal loop duct system for which there exists analytical solution. In addition, the extended T-method is employed to compute the loop duct system of a real building with an area of 380$m^2$. The results show that the computed flow rate at the exit differs from the designed flow rate by a range of -13.6~43.5 %. Consequently, three design factors must be adjusted in order that the flow rate may be balanced. These include the duct sizes, in terms of their lengths and diameters, the sub-duct locations and the positioning of damper which is found upstream of the exit duct.