Effective and accurate diagnosis of Alzheimer’s disease (AD), as well as early-stage detection, has gained more and more attention in recent years. For AD classification, we propose a new hybrid method for early detection of Alzheimer’s disease (AD) using Polar Harmonic Transforms (PHT) and Self-adaptive Differential Evolution Wavelet Neural Network (SaDE-WNN). The orthogonal moments are used for feature extraction from the grey matter tissues of structural Magnetic Resonance Imaging (MRI) data. Irrelevant features are removed by the feature selection process through evaluating the in-class and among-class variance. In recent years, WNNs have gained attention in classification tasks; however, they suffer from the problem of initial parameter tuning, parameter setting. We proposed a WNN with the self-adaptation technique for controlling the Differential Evolution (DE) parameters, i.e., the mutation scale factor (F) and the cross-over rate (CR). Experimental results on the Alzheimer’s disease Neuroimaging Initiative (ADNI) database indicate that the proposed method yields the best overall classification results between AD and mild cognitive impairment (MCI) (93.7% accuracy, 86.0% sensitivity, 98.0% specificity, and 0.97 area under the curve (AUC)), MCI and healthy control (HC) (92.9% accuracy, 95.2% sensitivity, 88.9% specificity, and 0.98 AUC), and AD and HC (94.4% accuracy, 88.7% sensitivity, 98.9% specificity and 0.99 AUC).