Thermal grease gets generally application in power device, for its high-efficient thermal conducting performance. While in the long-term operating situation, thermal grease will degrade with the pump-out and dry-out phenomenon and do harm to the heat dissipation of the devices, so it is necessary to monitor the states of thermal grease. In this paper, we propose a method to monitor the thermal resistance of thermal grease using the cooling curves of junction temperature. By establishing the relationship between the RC parameters of Cauer network and time constants of cooling curves, the thermal parameters about thermal grease can be obtained. Experimental tests are performed to verify the accuracy of proposed method. Results indicate the degradation of thermal grease can be monitored by detecting the variation of thermal resistance.