This paper presents a torque tracking impedance control strategy for a lower limb rehabilitation robot (LLRR) with three joints, hip, knee and ankle. The strategy allows the human-robot system to track a desired interaction torque. To track the desired torque, the robot reference trajectory and actuator torque are designed properly based on the torque tracking impedance control. A constant torque tracking experiment performed on a healthy male subject has shown that the maximum normalized root mean square deviation (NRMSD) of each joint is less than 32%. It indicates that the control strategy is feasible and the LLRR is capable of providing stroke patients with active rehabilitation training.