In this study, the technique associated with the capturing involuntary changes in voice elements caused by diseases is applied to diagnose them and a voice index is proposed to discriminate mild cognitive impairments. The participants in this study included 399 elderly people aged 65 years or older living in Matsumoto City, Nagano Prefecture, Japan. The participants were categorized into healthy and mild cognitive impairment groups based on clinical evaluation. It was hypothesized that as dementia progressed, task performance would become more challenging, and the effects on vocal cords and prosody would change significantly. In the study, voice samples of the participants were recorded while they were engaged in mental calculational tasks and during the reading of the results of the calculations written on paper. The change in prosody during the calculation from that during reading was expressed based on the difference in the acoustics. Principal component analysis was used to aggregate groups of voice features with similar characteristics of feature differences into several principal components. These principal components were combined with logistic regression analysis to propose a voice index to discriminate different mild cognitive impairment types. Discrimination accuracies of 90% and 65% were obtained for discriminations using the proposed index on the training and verification data (obtained from a population different from the training data), respectively. Therefore, it is suggested that the proposed index may be utilized as a means for discriminating mild cognitive impairments.