Deep learning has shown impressive diagnostic abilities in Alzheimer’s disease (AD) research in recent years. However, although neuropsychological tests play a crucial role in screening AD and mild cognitive impairment (MCI), there is still a lack of deep learning algorithms only using such basic diagnostic methods. This paper proposes a novel semi-supervised method using neuropsychological test scores and scarce labeled data, which introduces difference regularization and consistency regularization with pseudo-labeling. A total of 188 AD, 402 MCI, and 229 normal controls (NC) were enrolled in the study from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. We first chose the 15 features most associated with the diagnostic outcome by feature selection among the seven neuropsychological tests. Next, we proposed a dual semi-supervised learning (DSSL) framework that uses two encoders to learn two different feature vectors. The diagnosed 60 and 120 subjects were randomly selected as training labels for the model. The experimental results show that DSSL achieves the best accuracy and stability in classifying AD, MCI, and NC (85.47% accuracy for 60 labels and 88.40% accuracy for 120 labels) compared to other semi-supervised methods. DSSL is an excellent semi-supervised method to provide clinical insight for physicians to diagnose AD and MCI.