The one-leg stance is frequently used in balance training and rehabilitation programs for various balance disorders. There are some typical one-leg stance postures in Tai Chi (TC) and yoga, which are normally used for improving balance. However, the mechanism is poorly understood. Besides, the differences of one-leg stance postures between TC and yoga in training balance are still unknown. Therefore, the aim of the present study was to investigate cortical activation and rambling and trembling trajectories to elucidate the possible mechanism of improving one-leg stance balance, and compare the postural demands during one-leg stance postures between TC and yoga. Thirty-two healthy young individuals were recruited to perform two TC one-leg stance postures, i.e., right heel kick (RHK) and left lower body and stand on one leg (LSOL), two yoga postures, i.e., one-leg balance and Tree, and normal one-leg standing (OLS). Brain activation in the primary motor cortex, supplementary motor area (SMA), and dorsolateral prefrontal cortex (DLPFC) was measured using functional near-infrared spectroscopy. The center of pressure was simultaneously recorded using a force platform and decomposed into rambling and trembling components. One-way repeated-measures analysis of variance was used for the main effects. The relative concentration changes of oxygenated hemoglobin (ΔHbO) in SMA were significantly higher during RHK, LSOL, and Tree than that during OLS (p < 0.001). RHK (p < 0.001), LSOL (p = 0.003), and Tree (p = 0.006) all showed significantly larger root mean square rambling (RmRMS) than that during OLS in the medial–lateral direction. The right DLPFC activation was significantly greater during the RHK than that during the Tree (p = 0.023), OLB (p < 0.001), and OLS (p = 0.013) postures. In conclusion, the RHK, LSOL, and Tree could be used as training movements for people with impaired balance. Furthermore, the RHK in TC may provide more cognitive training in postural control than Tree and OLB in yoga. Knowledge from this study could be used and implemented in training one-leg stance balance.