As Alzheimer’s disease (AD) is featured with degeneration and irreversibility, the diagnosis of AD at early stage is important. In recent years, some researchers have tried to apply neural network (NN) to classify AD patients from healthy controls (HC) based on functional MRI (fMRI) data. But most study focus on a single NN and the classification accuracy was not high. Therefore, this paper used the random neural network cluster which was composed of multiple NNs to improve classification performance. Sixty one subjects (25 AD and 36 HC) were acquired from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. This method not only could be used in the classification, but also could be used for feature selection. Firstly, we chose Elman NN from five types of NNs as the optimal base classifier of random neural network cluster based on the results of feature selection, and the accuracies of the random Elman neural network cluster could reach to 92.31% which was the highest and stable. Then we used the random Elman neural network cluster to select significant features and these features could be used to find out the abnormal regions. Finally, we found out 23 abnormal regions such as the precentral gyrus, the frontal gyrus and supplementary motor area. These results fully show that the random neural network cluster is worthwhile and meaningful for the diagnosis of AD.