A new method is presented to determine the structural damping. Through analyzing the radiation sound pressure of a plate, the attenuation ratio of the level of sound pressure is equal to that of the level of vibration when the structure vibrated freely. Based on the conclusion a valid method of determining structural damping through the measurement of sound attenuation time is presented . The structural loss factors, which are determined individually by using the new method and the traditional method, are almost equal to each other in the interested band of frequency. The analysis and experimentation show that the new method is correct, and can measure the damping of structure without contact.