Aiming at enhanced suppression of external disturbances and high-precision trajectory tracking of parallel SCARA robot dedicating to fast pick-and-place operations, this work presents the integrated control design of iterative learning algorithm, adaptive control and fuzzy rules, namely, fuzzy adaptive iterative learning control, for such type of robots. A step-design approach is adopted to ensure the adaptability of the designed control law, which is reflected in two aspects: ① the feedback gain of the controller is adjusted by the fuzzy rules; ② the adaptive unknown parameters are obtained by means of iterative learning estimation to suppress the uncertainties and external disturbances. The stability of the designed controller is analyzed and proved by the Lyapunov theory, and the effectiveness is verified by observing the tracking errors in joint space along with the testing pick path, in comparison with different iterative learning based algorithms. After the first-iteration learning, the motion errors of the four actuated joints can be reduced by 56.5%, 45.8%, 46.4% and 39.8%, respectively, and after 15 iterations of learning control, the final angular errors by the designed control law converge to 0.7×10−4 degree maximally. The varying maximum, root-mean-squared and mean angular displacement errors of the actuation joints can converge to zero values with the increasing iterations rapidly, which shows the robustness, effectiveness and advantages of the designed control law. The designed control law can be generalized to high-speed parallel pick-and-place robot to ensure high-precision trajectory tracking for high-quality material handling tasks.