The invention provides a numerically controlled demonstration instrument for demonstrating gear transmission failure, which comprises a gear failure characteristic assembly (1), a frame (20), a vibrating sensor (19), a magnetic powder clutch (14), a force sensor, a gear shifting system, a motor driving system, a numerical control system, and a data collection and processing system. The gear failure characteristic assembly (1) is installed on a transmission shaft (3), and the two ends of the transmission shaft are respectively installed on the frame (20) through a bearing seat. The instrument integrates gear failure, rotational efficiency and rotational precision, and is compact in structure and small in volume. Moreover, the instrument can not only demonstrate vibration mode phenomenon arising from gear failure behaviors in a gear transmission system, but also realize experimental teaching of the influence of different gear failure behaviors on gear transmission efficiency and transmission accuracy, so as to broaden the experimental contents for systematically teaching the gear transmission.