Rule selection is an important skill for human social life. We previously showed that stimulus-appropriate rule selection ability is attainable by age 7, using a rule management task consisting of three conditions with different rule processing requirements (TaskA: control, TaskB: single rule selection, TaskC: multiple rule selection) (Harada et al. 2018). However, the neural development subserving this rule processing system is not well understood. Here, we examined that development in the appropriate rule selection process in 55 children aged 7 to 10 years (mean age 8.7 ± 0.9 years, 33 girls), using the 42-channel fNIRS imaging system that measures oxygenated hemoglobin (oxy-Hb) covering the bilateral PFC and PMC. Task performances and cerebral hemoglobin changes in each region of interest (ROI) were analyzed as independent variable and age, task condition, age×task condition, and IQ as dependent variables by multiple regression analysis. The present study mainly focused on the effect of age in TaskC, as compared to TaskA and TaskB. The results showed that all effects on accuracy were significant (p<0.05) except for IQ. This showed that the ability to select stimulus-appropriate rule was developed from 7 to 10 years. In addition, the effect of age on TaskC-related cortical activity was observed only in the right frontopolar cortex (p=0.034), where activity decreased with age. Thus, it is suggested that the frontopolar cortex potentially plays an important role in the development of such a rule-based cognitive control system.