In Alzheimer’s diagnosis field, Computer-Aided Diagnosis (CADx) technology can improve the work performance of medical researchers and practitioners since it gives early chances to patient’s eligibility for clinical trials. The aim of this study is to develop a novel CADx system for the diagnosis of Alzheimer’s disease (AD) by utilizing genetic programming (GP) as data-driven evolutionary computation based modeling. The proposed method invokes a majority voting based scheme to select a set of most discriminant features which leads to the highest diagnosis accuracy of the final classification. The effectiveness of GP in categorizing patients with Alzheimer’s versus healthy group was revealed by developing models according to their performance in terms of higher-order spectra (HOS) features. The results show that the GP method achieved better performance compared to other the-state-of-the-art approaches. It is also found that the highest accuracy index was yielded by using the proposed data-driven modeling technique. The results of this study emphasize the practicality of GP-based method for developing CADx systems, on the basis of spontaneous speech analysis; can efficiently assist in the diagnosis of Alzheimer’s disease.