Summary: For the trajectory-tracking control of dynamic systems with unidentified parameters, a higher-order iterative learning control method is presented in the paper. In contrast to other known methods, the proposed learning control scheme can utilize more than one past error history contained in the trajectories generated at prior iterations. A convergency proof is given and it is also shown that the convergence speed can be improved in comparison with conventional methods. Examples are provided to show effectiveness of the algorithm, and, via simulation, it is demonstrated that the method yields a good performance even in the presence of disturbances.