Time-resolved near-infrared spectroscopy (TRS) enables assessment of baseline concentrations of hemoglobin (Hb) in the prefrontal cortex, which reflects regional cerebral blood flow and neuronal activity at rest. In a previous study, we demonstrated that baseline concentrations of oxy-Hb, deoxy-Hb, total-Hb, and oxygen saturation (SO2) measured by TRS were correlated with mini mental state examination (MMSE) scores. In the present study, we investigated whether Hb concentrations measured with TRS at rest can predict MMSE scores in aged people with various cognitive functions. A total of 202 subjects (87 males, 115 females, age 73.4 ± 13 years) participated. First, MMSE was conducted to assess cognitive function, and then baseline concentrations of oxy-Hb, deoxy-Hb, total-Hb, and SO2 in the bilateral prefrontal cortex were measured by TRS. Then, we employed the deep neural network (DNN) to predict the MMSE score. From the comparison results, the DNN showed 91.5% accuracy by leave-one-out cross validation. We found that not only the baseline concentration of SO2 but also optical path lengths contributed to prediction of the MMSE score. These results suggest that TRS with the DNN is useful as a screening test for cognitive impairment.