This study proposes a new cerebral lateralization index (LI) on the basis of neural activation intensity. Eight right-handed male college students (mean age 23.5 years) and 10 right-handed male college students (the mean age 25.1 years) participated in this study of visuospatial and verbal tasks, respectively. Functional brain images were taken from 3T MRI using the single-shot EPI method. A cerebral LI based on neural activation area (i.e., number of activated voxels) and another based on neural activation intensity (i.e., intensity of BOLD (blood oxygen level dependent)) were calculated for both cognition tasks. The result of calculating a cerebral LI based on neural activation area suggested that the right hemisphere is dominant during visuospatial tasks and the left hemisphere is dominant during verbal tasks. When a cerebral LI was computed on the basis of the neural activation intensity, it was shown that the area of cerebral lateralization closely related to visuospatial tasks is the superior parietal lobe, and the area of cerebral lateralization closely related to verbal tasks is the inferior and middle frontal lobe. Since the proposed method can determine the dominance of the cerebrum by each area, it can be helpful to determine cerebral lateralization accurately and easily.