The relationships between Japanese Alzheimer’s disease (AD) patients and their mitochondrial single nucleotide polymorphism (mtSNP) frequencies at individual mtDNA positions of the entire mitochondrial genome are described using the radial basis function (RBF) network and the modified method. Japanese AD patients are associated with the haplogroups G2a, B4c1, and N9b1. In addition, to compare mitochondrial haplogroups of the AD patients with those of other classes of Japanese people, the relationships between four classes of Japanese people (i.e., Japanese centenarians, Parkinson’s disease (PD) patients, type 2 diabetic (T2D) patients, and non-obese young males) and their mtSNPs are also described. The four classes of people are associated with following haplogroups: Japanese centenarians—M7b2, D4b2a, and B5b; Japanese PD patients—M7b2, B4e, and B5b; Japanese T2D patients—B5b, M8a1, G, D4, and F1; and Japanese healthy non-obese young males—D4g and D4b1b. The haplogroups of the AD patients are therefore different from those of the other four classes of Japanese people. As the analysis method described in this article can predict a person’s mtSNP constitution and the probabilities of becoming an AD patient, centenarian, PD patient, or T2D patient, it may be useful in initial diagnosis of various diseases.