A large battery of neurocognitive tests are used to detect cognitive impairment and classify early mild cognitive impairment (EMCI), late mild cognitive impairment (LMCI), and Alzheimer’s Disease (AD) from cognitive normal (CN). The goal of this study was to develop a deep learning algorithm to identify a few top neurocognitive tests that can accurately classify these four groups. We also derived a simplified risk-stratification score model for classification. Over 100 variables that included neuropsychological/neurocognitive tests, demographics, genetic factors, and blood biomarkers were collected from 383 EMCI, 644 LMCI, 394 AD patients, and 516 cognitive normal from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. A neural network algorithm was trained on data split 90% for training and 10% testing. We evaluated five different feature selection methods. Prediction performance used area under the curve (AUC) of the receiver operating characteristic analysis. The five different feature selection methods consistently yielded the top classifiers to be the Clinical Dementia Rating Scale - Sum of Boxes (CDRSB), Delayed total recall (LDELTOTAL), Modified Preclinical Alzheimer Cognitive Composite with Trails test (mPACCtrailsB), the Modified Preclinical Alzheimer Cognitive Composite with Digit test (mPACCdigit), and Mini-Mental State Examination (MMSE). The best classification model yielded an AUC of 0.984, and the simplified risk-stratification score yielded an AUC of 0.962 on the test dataset. The deep-learning algorithm and simplified risk score derived from our deep-learning algorithm accurately classifies EMCI, LMCI, AD and CN patients using a few commonly available neurocognitive tests.