Various rehabilitation robots have been employed to recover the motor function of stroke patients. To improve the effect of rehabilitation, robots should promote patient participation and provide compliant assistance. This paper proposes an adaptive admittance control scheme (AACS) consisting of an admittance filter, inner position controller, and electromyography (EMG)-driven musculoskeletal model (EDMM). The admittance filter generates the subject's intended motion according to the joint torque estimated by the EDMM. The inner position controller tracks the intended motion, and its parameters are adjusted according to the estimated joint stiffness. Eight healthy subjects were instructed to wear the ankle exoskeleton robot, and they completed a series of sinusoidal tracking tasks involving ankle dorsiflexion and plantarflexion. The robot was controlled by the AACS and a non-adaptive admittance control scheme (NAACS) at four fixed parameter levels. The tracking performance was evaluated using the jerk value, position error, interaction torque, and EMG levels of the tibialis anterior (TA) and gastrocnemius (GAS). For the NAACS, the jerk value and position error increased with the parameter levels, and the interaction torque and EMG levels of the TA tended to decrease. In contrast, the AACS could maintain a moderate jerk value, position error, interaction torque, and TA EMG level. These results demonstrate that the AACS achieves a good tradeoff between accurate tracking and compliant assistance because it can produce a real-time response to stiffness changes in the ankle joint. The AACS can alleviate the conflict between accurate tracking and compliant assistance and has potential for application in robot-assisted rehabilitation.