The turbogenerator vibration faults have the character of variety. Many faults often occur synchronously. The traditional BP neural network can diagnose the single fault effectively. If we diagnose the multiple faults by using the BP neural network, we must train all samples of multiple faults, which is will increase the number of training samples and the burden of learning greatly. So the diagnosis can not be performed easily. This paper introduces a method based on SOM neural network, which is studied by using the single sample and diagnosing the multiple faults according to the position of output nerve cell. By analyzing the examples, the method is proved to be available for diagnosing the multiple faults of Turbogenerator set.