This paper presents the modeling and simulation of a lower limb exoskeleton, where the robot is designed with six rotational degrees of freedom that include joints of the two legs, with support at the hip. A three-dimensional structural model was built in Solid Works and its mathematical model was carried out using the W. Khalil and E. Dombre methodology. The exoskeleton tracked human gait trajectories for each joint using a computed torque control (CTC). The results showed stability in the controller, and a maximum joint mean square error of 1.4x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> m in the path tracking, for all joints. Therefore, the CTC simulated and the modeling of this exoskeleton can be used in gait rehabilitation tasks.