Alzheimer＇s　disease　(AD)　is　a　progressive　neurodegenerative　disease,　and　mild　cognitive　impairment　(MCI)　is　a　transitional　stage　between　normal　control　(NC)　and　AD.　A　multiclass　classification　of　AD　is　a　difficult　task　because　there　are　multiple　similarities　between　neighboring　groups.　The　performance　of　classification　can　be　improved　by　using　multimodal　data,　but　the　improvement　could　be　limited　with　inefficient　fusion　of　multimodal　data.　This　study　aims　to　develop　a　framework　for　AD　multiclass　diagnosis　with　a　linear　discriminant　analysis　(LDA)　scoring　method　to　fuse　multimodal　data　more　efficiently.　Magnetic　resonance　imaging,　positron　emission　tomography,　cerebrospinal　fluid　biomarkers,　and　genetic　features　were　first　preprocessed　by　performing　age　correction,　feature　selection,　and　feature　reduction.　Then,　they　were　individually　scored　using　LDA,　and　the　scores　that　represent　the　AD　pathological　progress　in　different　modalities　were　obtained.　Finally,　an　extreme　learning　machine-based　decision　tree　was　established　to　perform　multiclass　diagnosis　using　these　scores.　The　experiments　were　conducted　on　the　AD　Neuroimaging　Initiative　dataset,　and　accuracies　of　66.7%　and　57.3%　and　F1-scores　of　64.9%　and　55.7%　were　achieved　in　three-　and　four-way　classifications,　respectively.　The　results　also　showed　that　the　proposed　framework　achieved　a　better　performance　than　the　method　that　did　not　score　multimodal　data　and　the　methods　in　previous　studies,　thereby　indicating　that　the　LDA　scoring　strategy　is　an　efficient　way　for　multimodalities　fusion　in　AD　multiclass　classification.