The fault diagnosis of generator units is critical to guarantee the high efficiency of the electric system. However, detailed fault samples are difficult to obtain, and the distribution of fault samples usually shows the characteristics of unevenness and unbalance, which may lead to low fault diagnosis precision. Nevertheless, it has been seldom considered in the traditional classifier of fault diagnosis for generator units until now. In this paper, a novel fault classifier of weighted support vector data description (SVDD) with fuzzy adaptive threshold decision is proposed and applied in the fault diagnosis of generator units. To tackle the drawback that SVDD is sensitive to the distribution of samples, a novel SVDD model based on a complex weight is proposed. The complex weight is assigned with local density and size-based weight, while local density of each data point is obtained with the k-nearest neighbour approach and the size-based weight of each data point is computed according to the proportion of classes. Then the conventional SVDD is reformulated with the complex weights. Furthermore, new decision rules based on the relative distance and fuzzy adaptive threshold decision are applied to identify the class of testing samples. Finally, the proposed method is applied in the identification of several standard datasets, as well as the fault diagnosis for a turbo-generator unit. Experimental results and the engineering application reveal that the proposed method shows good performance in accuracy and universality, and is suitable for the fault diagnosis of generator units.