This invention provides a lower-limb off-axis movement training apparatus, which is mounted on the movement part of a sagittal plane exercise machine and allows the user to perform off-axis movement training during sagittal plane functional movements. The said apparatus for the lower limb off-axis training consists of a base, an off-axis movement generating part mounted on the base, and a foot container supported by the off-axis movement generating part. The said off-axis movement generating part comprising at least one of the following two: (1) off-axis pivoting generating part, which generates the pivoting movement of the foot container; (2) off-axis sliding generating part, which generates the sliding movement of the foot container. A feedback training system including the said training apparatus is provided. While the user performs sagittal plane movements of the lower limbs, the said system provides off-axis movement training integrated with the sagittal plane movements. The invented off-axis training apparatus and system can be used to help human subjects improve off-axis and sagittal plane neuromuscular control, reduce the incidence of lower limb injuries and facilitate post-injury rehabilitation.