Postural instability and falls are commonly seen because of aging and motor disabilities. This study aims to assess the posture-related changes in brain functional connectivity by wavelet phase coherence (WPCO) of oxyhemoglobin concentration change ($Δ$[HbO2]) signals measured through near-infrared spectroscopy (NIRS) in elderly subjects. The NIRS signals were continuously recorded from the prefrontal cortex and sensorimotor cortical areas in 39 healthy elderly subjects and 22 young healthy subjects during 20 min resting and 10 min standing states. Eight connection types were obtained from the recorded brain areas. The WPCO were calculated in five frequency intervals in each channel pair as follows: I, 0.6–2 Hz; II, 0.145–0.6 Hz; III, 0.052–0.145 Hz; IV, 0.021–0.052 Hz; and V, 0.0095–0.021 Hz. Results show that posture change and age significantly interacts with the right prefrontal cortex (PFC) and left sensorimotor cortex (SMC) connectivity in interval V (F = 5.010, p = 0.028). The left and right PFC connectivity in interval I, the left and right SMC connectivity in interval IV, and the connectivity in interval V, including right PFC and right SMC connectivity, left PFC and left SMC connectivity, and right PFC and left SMC connectivity, showed a significant difference between the Group Elderly and Group Young in response to posture change (p < 0.05). This study provides new insight into the mechanism of posture control, and results may be useful in assessing the risk of postural instability in aged persons.