The health assessment of power equipment can reduce the blindness of equipment maintenance. Aiming at the problem of high ambiguity of state division near the boundary point of adjacent states in current circuit breaker state evaluation, a method for evaluating the state of circuit breaker with extension gray cloud clustering considering the difference of state interval is designed in this paper. This method uses extension cloud theory and gray cloud clustering function as the basic theoretical framework, adopts different constraint ranges to construct the optimal cloud entropy, and simultaneously considers the difference in the state interval range. Taking a vacuum circuit breaker in a substation as an example, in the early warning state, the cloud entropy constructed by the "3En" rule is 0.6712, and the cloud entropy constructed by the "50% correlation" rule is 0.5776. The optimal cloud entropy constructed in this paper is 0.6127. This method will The overall judgment is an early warning state, which is consistent with the results of other evaluation methods, but its reflection on the degree of membership is more accurate. The analysis of the example results shows that it can effectively deal with the uncertain factors in the evaluation of the circuit breaker's status, and has high feasibility. At the same time, the accuracy of the evaluation results has been improved to a certain extent.