The number of patients with Alzheimer's disease is increasing rapidly every year. Scholars often use computer vision and machine learning methods to develop an automatic diagnosis system.In this study, we developed a novel machine learning system that can make diagnoses automatically from brain magnetic resonance images.First, the brain imaging was processed, including skull stripping and spatial normalization. Second, one axial slice was selected from the volumetric image, and stationary wavelet entropy (SWE) was done to extract the texture features. Third, a single-hidden-layer neural network was used as the classifier. Finally, a predator-prey particle swarm optimization was proposed to train the weights and biases of the classifier.Our method used 4-level decomposition and yielded 13 SWE features. The classification yielded an overall accuracy of 92.73±1.03%, a sensitivity of 92.69±1.29%, and a specificity of 92.78±1.51%. The area under the curve is 0.95±0.02. Additionally, this method only cost 0.88 s to identify a subject in online stage, after its volumetric image is preprocessed.In terms of classification performance, our method performs better than 10 state-of-the-art approaches and the performance of human observers. Therefore, this proposed method is effective in the detection of Alzheimer's disease.