Motor dynamics in Antagonistic Variable Stiffness Actuator (AVSA) is generally not considered in control system design. This ignorance can lead to an inaccurate system model and hence the performance of closed-loop system can be affected. The motor dynamics can be modeled as an input-delay in actuator model. For the first time, motor dynamics is modeled as input time-delay for an antagonistic variable stiffness actuator in this paper. Since the stiffness of AVSA is a nonlinear function of system states, stiffness tracking for AVSA is a challenging task. Especially when the model contains input delay, many of the existing delay compensation controllers cannot be used for stiffness tracking purpose. To handle this issue, a nonlinear transformation is introduced and then a super-twisting sliding mode control is utilized to reach position and stiffness tracking simultaneously. To compensate input time-delay, prediction-based feedback is involved together with disturbance observers for estimating external disturbance. Simulation results show that the proposed design approach is successful in position and stiffness tracking and at the same time in attenuating external disturbance effect.