Rehabilitation strategies based on robotic systems, like lower-limb exoskeletons, is expected to reduce the burden of locomotor impairment in patients with neurological diseases. In this work, we present the preliminary results of a trajectory tracking impedance control method applied to the ExoRoboWalker, a six degree-of-freedom (DoF) exoskeleton. The wearable robot was developed as an over-ground gait trainer to aid children and young adults with Cerebral Palsy (CP) achieve physiological gait patterns. The experiments were carried out in three healthy adults walking over-ground with the system working in three different modes: First, with the exoskeleton’s motors unpowered, to assess the system’s backdrivability, user-robot interaction and subject gait pattern; second, with the exoskeleton working in "transparent" mode; and finally, with the system working with the proposed impedance controller. As expected, when the exoskeleton is unpowered, the system presents low backdrivability, thereby resulting in high user-robot interaction torques and a nonphysiological gait pattern. However, the results show that the system was able to partially restore the subjects gait pattern and reduce the user-robot interaction torque when set in "transparent" mode. Finally, while working with the trajectory tracking impedance controller, the ExoRoboWalker was able to guide the subject through a target trajectory. This is the first step towards use the system as an over-ground gait trainer in CP population.