Gait rehabilitation is essential for chronic stroke patients to regain independent walking ability and quality of life, of which symmetry is regarded as a gold standard of gait quality. In this letter, a cable-driven lower limb exoskeleton powered by series elastic actuators (SEAs) has been developed, and a generalized gait-phase-based assistive strategy has been presented to enhance the gait symmetry of chronic stroke patients in the future. This strategy features a parameterized assistive force generation method that allows individuals customization to achieve more synchronized assistance with their walking gait patterns. A compliant human-robot interaction is guaranteed by SEA, and the exoskeleton exhibits low passive impedance and good transparency. The proposed assistive strategy was evaluated with five able-bodied subjects walking with the assistance from exoskeleton while adding artificial impairments to mimic a pathological gait with deficits (i.e., reduced knee flexion and foot-drop). Experimental results proved its efficacy in enhancing temporal walking gait symmetry to the levels comparable to participants’ normal gait.