In this paper, we propose a novel adaptive feedforward super-twisting sliding mode control algorithm to resolve the tracking control problem of parallel manipulators. The proposed control scheme includes three main terms, (i) the standard super-twisting algorithm, (ii) an adaptive feedforward dynamic model, and (iii) a feedback term to ensure stability. The proposed controller provides robustness towards uncertainties and disturbances, less sensitive to measurement noise, and allows dynamic parameters adaptation of the manipulator while executing a certain task. Real-time experiments are conducted on a 3-DOF non-redundant Delta parallel robot, including two main scenarios, (i) nominal case, and (ii) robustness towards operating acceleration changes. The relevance of the proposed controller is verified experimentally in both scenarios and compared with two other controllers from the literature, including the standard and the feedforward super-twisting sliding mode control algorithms.