According to human biomechanics study, ankle joint musculoskeletal structure constantly changes joint stiffness during walking. Being inspired by human biomechanics, an ankle exoskeleton robot with an adjustable stiffness, named VSAnkleExo was designed and by using Simulation Environment MATLAB/SimMechanics, its position tracking simulation tests were carried out in this study. VSAnkleExo is intended to be used for the purposes of walking aid and rehabilitation. An effective position control of the robot is required for these purposes. Therefore, in this study, before testing the recommended controllers on the real robot, the position control simulations were applied on MATLAB/SimMechanics model of the robot. It is not easy to obtain the mathematical model of the robot because VSAnkleExo has a complex structure. For this reason, the control methods that do not need the mathematical model of the robot are tested here. In this study, firstly, a robot model was created by using MATLAB/SimMechanics. Then, trajectory tracking experiments and response experiments with disturbance were carry out on the model in order to reveal the efficiency of proposed fuzzy logic controllers. Besides, these experiments were performed with conventional PID and the all experiment results were compared. Experimental results show that proposed fuzzy PD+PID controller can influentially decrease reference tracking errors and acquire appropriate control performance. Furthermore, the controller is robust against external forces.