Quadrotor unmanned aerial vehicles (UAVs) have been developed and applied into several types of workplaces, such as warehouses, which usually involve human workers. The co-existence of human and UAVs brings new challenges to UAVs: potential failure of UAVs may cause risk and danger to surrounding human. Effective and efficient detection of such failure may provide early warning to the surrounding human workers and reduce such risk to human beings as much as possible. One of the commonest reasons that cause the failure of the UAV's flight is the physical damage to the propellers. This paper presents a method to detect the propellers' damage only based on the audio noise caused by the UAV's flight. The diagnostic model is developed based on convolutional neural network (CNN) and transfer learning techniques. The audio data is collected from the UAVs in real time, transformed into the time-frequency spectrogram, and used to train the CNN-based diagnostic model. The developed model is able to detect the abnormal features of the spectrogram and thus the physical damage of the propellers. To reduce the data dependence on the UAV's dynamic models and enable the utilization of the training data from UAVs with different dynamic models, the CNN-based diagnostic model is further augmented by transfer learning. As such, the refinement of the well-trained diagnostic model ground on other UAVs only requires a small amount of UAV's training data. Experimental tests are conducted to validate the diagnostic model with an accuracy of higher than 90%.