The invention relates to a method and a device for online monitoring and diagnosis on insulation state of a gas insulated switchgear (GIS) invaded by steep waves. The method comprises the following steps that S1, a narrow-band current sensor and a wide-band high-frequency current sensor are sleeved on a grounding line of a GIS device; S2, ultrasonic wave sensors are distributed beside supporting insulators of all gas chambers respectively; S3, the narrow-band current sensor receives signals with frequency ranging from 20kHz to 3MHz, time is recorded as T1, the largest amplitude is recorded as A1, the wide-band high-frequency current sensor receives signals with frequency ranging from 1MHz-50MHz, time is recorded as T2, the largest amplitude is recorded as A2, A=A1-A2, and T= (T1+T2)/2; S4, if A is larger than zero, insulation damage to the GIS is small, and monitoring is performed continuously; S5, if A is smaller than zero, an alarm is given out. Types of insulation damage to the GIS are determined according to characteristic parameters. By means of an acoustoelectric combination mode, the insulation state of the GIS devices invaded by steep wave voltage is monitored in an online mode, and insulation damage to the GIS devices is monitored in real time. Therefore, the method and the device for online monitoring and diagnosis on the insulation state of the GIS invaded by steep waves have important significance in improving safety and reliability of operation of power systems.