Alzheimer's Disease (AD), which is left untreated, is the primary cause of neurodegenerative dementia, which primarily affects those over 65. Memory and thought processes are gradually disrupted by the irreversible brain disruption and, eventually, the capacity to fulfil simple tasks. Detecting AD early prevents its progression and diminishes its signs. The study aimed to build a classification model that might predict the early stages of Alzheimer's disease using accurate early-stage gene expression data from blood obtained from a clinical Alzheimer's dataset. The datasets used in this work were gathered from the Gene Expression Omnibus (GEO) and are GSE63060 and GSE63061.It has the right rows for (569 samples) and columns for (16382 genes). The suggested GWO gene selection method aims to identify the ideal feature subset for medical data. A model for predicting early Alzheimer's disease is proposed based on the modified Grey Wolf Optimizer and Support Vector Machine (GWO-SVM). These methods will help reduce the number of trivial and redundant genes in the original datasets. We attained an accuracy of 82%-88% using only the Support Vector Machine method. When we utilized several evolutionary algorithms to implement gene selection, we observed an increase in accuracy of 6%-11%, with modified Grey Wolf optimization with Crossover (CGWO) called the proposed algorithm (CGWO-SVM) achieving the highest accuracy of (97.41%) with the Alzheimer's disease dataset in comparison to the other competitive schemes in the existing literature. Thus, the proposed system is suitable for picking more accurate classification and interesting genes to increase classification accuracy while decreasing gene dimensions.