Optical topography (OT) based on near infrared spectroscopy (NIRS) is suitable for measuring changes in the concentrations of oxygenated hemoglobin (oxy-Hb) and deoxygenated hemoglobin (deoxy-Hb) in tissue in the brain. It can be used to investigate brain functions of subjects of all ages because it is non-invasive and less constraining on subjects. Conventional OT systems require optical fibers to irradiate light on the scalp and detect light transmitted through the tissues in the human head, but optical fibers limit subjects' movable ranges, so some portable measurement systems without optical fibers have been developed. We developed a prototype of a multi-channel portable OT system and used it to measure changes in the concentrations of oxy-Hb and deoxy-Hb in the frontal region of the cerebral cortex during a mental calculation. The results show typical changes in oxy-Hb and deoxy-Hb during a mental task and suggest that the prototype system can be used to investigate brain functions in the frontal region of the cerebral cortex.