For the waist assisting, this paper proposes a novel parallel back-support exoskeleton for rehabilitation or power augmentation (PBE-RePA), which is suitable for assisting many types of waist movements and reducing restrictions on daily activities. Considering repetitive waist movements, a time-delay estimation based dual model-free control with initial rectifying mechanism is designed for the trajectory tracking control of PBE-RePA. The system dynamics are reconstructed by ultra-local model while time-delay estimation is utilized to obtain the lumped unknown part in that model. To realize more accurate tracking, an adaptive iterative learning compensator is added to form a new dual model-free control structure, which has excellent control performance in time domain and can enable asymptotically precise tracking along iteration axis. Moreover, the identical initial condition is relaxed by introducing the initial rectifying mechanism to modify the reference trajectory. The virtual prototype of PBE-RePA is established as a platform for visualized co-simulation in MATLAB/Simscape Multibody. The results of two co-simulation cases demonstrate the effectiveness and robustness of the proposed algorithm.