An association between cognitive impairment and tripping over obstacles during locomotion in older adults has been suggested. However, owing to its memory-guided movement, whether this is more pronounced in the trailing limb is poorly known. We examined age-related changes in stepping over, focusing on trailing limb movements, and their association with cognitive performance. Age-related changes in obstacle avoidance were examined by comparing the foot kinematics of 105 older and 103 younger adults when stepping over an obstacle. The difference in the clearance between the leading and trailing limbs (Δ clearance) was calculated to determine the degree of decrement in the clearance of the trailing limb. A cognitive test battery was used to evaluate cognitive function among older adults to assess their association with Δ clearance. Older adults showed a significantly lower clearance of the trailing limb than young adults, resulting in greater Δ clearance. Significant correlations were observed between greater Δ clearance and scores on the Montreal Cognitive Assessment and immediate recall of the Wechsler Memory Scale-Revised Logical Memory test. Therefore, memory functions may contribute to the control of trailing limb movements, which can secure a safety margin to avoid stumbling over an obstacle during obstacle avoidance locomotion.