Computer-aided diagnosis of dementia using a support vector machine (SVM) can be improved with feature selection. The relevance of individual features can be quantified from the SVM weights as a significance map (p-map). Although these p-maps previously showed clusters of relevant voxels in dementia-related brain regions, they have not yet been used for feature selection. Therefore, we introduce two novel feature selection methods based on p-maps using a direct approach (filter) and an iterative approach (wrapper). To evaluate these p-map feature selection methods, we compared them with methods based on the SVM weight vector directly, t-statistics, and expert knowledge. We used MRI data from the Alzheimer's disease neuroimaging initiative classifying Alzheimer's disease (AD) patients, mild cognitive impairment (MCI) patients who converted to AD (MCIc), MCI patients who did not convert to AD (MCInc), and cognitively normal controls (CN). Features for each voxel were derived from gray matter morphometry. Feature selection based on the SVM weights gave better results than t-statistics and expert knowledge. The p-map methods performed slightly better than those using the weight vector. The wrapper method scored better than the filter method. Recursive feature elimination based on the p-map improved most for AD-CN: the area under the receiver-operating-characteristic curve (AUC) significantly increased from 90.3% without feature selection to 92.0% when selecting 1.5%-3% of the features. This feature selection method also improved the other classifications: AD-MCI 0.1% improvement in AUC (not significant), MCI-CN 0.7%, and MCIc-MCInc 0.1% (not significant). Although the performance improvement due to feature selection was limited, the methods based on the p-map generally had the best performance, and were therefore better in estimating the relevance of individual features.