In this study, a multi-motion self-balancing lower limb exoskeleton is designed to provide crutches-free rehabilitation training for quadriplegic patients on flat terrain without hand support. First, based on the biomechanical characteristics of the human body and the bionic mechanism configuration of the human lower limb, an exoskeleton with a full-drive series-parallel hybrid structure was established. Secondly, the D-H method, geometric method and Newton iteration method were used to establish the forward and reverse kinematic solutions of the exoskeleton. In addition, the static self-balancing principle was used to complete the planning of the multi-motion self-balancing trajectory. Finally, in order to verify the effectiveness of the proposed method, some numerical simulations were performed in this paper. The theoretical trajectories of the waist, ankle joint and foot center were compared with the simulated trajectories. The research results show that the forward and reverse kinematics model of the exoskeleton is feasible. Under the condition of contact force parameters, the exoskeleton has the ability of multi-motion self-balancing walking on flat terrain.