Pneumatic artificial muscle actuators possess great potential in compliant rehabilitation devices since they are flexible and lightweight. The inherent high nonlinearities, uncertainties, hysteresis and time-varying characteristics in pneumatic artificial muscle systems brings much challenge for accurate system modeling and controller design. The angle tracking problem based on iterative learning control technology is considered in this work. This research proposes a new initial-rectification adaptive iterative learning control scheme for a pneumatic artificial muscle-actuated device with nonzero initial errors and iteration-varying reference trajectories. A barrier Lyapunov function is used to deal with the constraint requirement. A new initial rectification construction method is given to solve the nonzero initial error problem. Nonparametric uncertainties in the system are approximated by using a neural network, whose optimal weight is estimated by using difference learning method. As the iteration number increases, the system states of angle and angular velocity can accurately track the reference trajectories over the whole interval, respectively. In the end, the simulation results show excellent trajectory tracking performance of the iterative learning controller even if the reference trajectories are non-repetitive over the iteration domain.